I would like some fun facts that include numbers. Like, idk, there are at least 30 million people living in the U.S. C? Anything like that izz fine. Thnx!!!
Gimme a random fun fact!?
1.elephants and humans are the only mammles that can stan on their heas!
2.when a frog throws up it throws up its stomach aswell and then swallows it back!
3.there are more telephones in the state of washington then people!
and you said to throw something at you...
4.one in 50 girls have 3rd nipple!!!! iwww(it usually looks like a tiny freckle!)
Reply:There are 293 ways to make change for a dollar.
A dime has 118 ridges around the edge.
There are 336 dimples on a regulation golf ball.
Monday, May 24, 2010
Survey: Just Random stuff.?
1.What's your middle name?
3. Would you rather spend a whole day with your mom or your dad?
4.Where will you be 12 hours from now?
5.Is it easy for others to make you feel awkward?
6.Do you know what you are going to wear tomorrow?
7.What serial killer do you find most disturbing?
8.When did your last relationship end?
9.Does anyone hate you for no reason?
10.Can you make yourself cry?
11.How many hours of sleep did you get last night?
12.Is your life simple or complicated?
13.Would you go back in time if you were given the chance?
14.What are your favorite colors?
16.Do you know anyone who lives in Wyoming?
17.Have you ever kissed someone whose name starts with a C?
18.Have you ever passed out from drinking too much?
19.What are you doing tomorrow?
20.Are you easily confused?
21.Do you think you would make a good parent?
22.What's your favorite kind of ice cream?
24.Are you taller than 5'4"?
Survey: Just Random stuff.?
1. Paul, the name that i use on here (Jeff is my first name)
3. my dad- I get along better with him
4.I'll probably be at my brother's
5. Yes
6. Haha, I won't know till tomorrow gets here.
7. Definitely, Jeffrey Dahmer. One of my friends did a powerpoint presentation on him, what I learned was absolutely disturbing
8. I broke up with my last ex a year ago, and have taken time to myself since then.
9.I'm sure there are people that don't like me, but I can't think of anyone who hates me.
10. Yes, I did theater, so I know how to do that.
11. 7 hours
12. Haha, I won't go there right now.
13. Yes, I would
14. blue, teal, silver, and green
16. No, I don't
17. No, my exs names start with A, B, and M
18. no, I've been drunk, but I've never passed out.
19. finishing getting ready for the holidays
20. Yes, very. When I lived with my friend in the city for 2 months, he used to draw me road maps so I wouldn't get lost, lol.
21. Honestly, no.
22. vanilla with caramel or hot fudge
24. Yes, I'm 6'0"
Have a great day and consider yourself starred! Happy holidays!
Reply:1florence
2??
3dad
4my best friends house
5very much so
6yes
7idk of any serial killers off the top of my head...
8never had one XD
9oh yes
10yup
11 11 hours =D
12complicated
13yes
14blue
15??
16nope
17nah
18no
19party!
20yes
21yep
22moose tracks =)
23?
24no, im 5'1"
Reply:1.
3.both
4.still in my house
5.not really
6.nope
7.Albert Fish
8.a year ago
9.some people do
10.nope
11.9hrs
12.complicated
13.yes
14.purple,lime green,black,turquoise
16.no
17.no
18.i don't drink
19.sleep,wrap presents,shop,eat
20.no
21.maybe
22.strawberry
24.yes
Reply:Bliss
Neither, they are both dead.
I don't know, I haven't got there yet.
No
No
None
1972
No
Yes
9
Simple
No
Blue and Grey
Yes
Yes
Yes
Won't know untill then
No
No
Soft
Yes
Reply:1.What's your middle name? I dont have one
3. Would you rather spend a whole day with your mom or your dad? DAD!!
4.Where will you be 12 hours from now? hmmm....idk
5.Is it easy for others to make you feel awkward? Kind of
6.Do you know what you are going to wear tomorrow? NO
7.What serial killer do you find most disturbing?All of them
8.When did your last relationship end? Never had one
9.Does anyone hate you for no reason? Ya!my french teacher hates me to death and i never said or did any thing 2 her!!
10.Can you make yourself cry? Ya,jus think of my life!
11.How many hours of sleep did you get last night? 51/2
12.Is your life simple or complicated?CoMpLiCaTeD
13.Would you go back in time if you were given the chance? Ya defante
14.What are your favorite colors?Blue and green
16.Do you know anyone who lives in Wyoming? Hmmm...NO
17.Have you ever kissed someone whose name starts with a C? I kiss anyone but my mom,dad,close friends,cousins
18.Have you ever passed out from drinking too much? I have no bad habits.
19.What are you doing tomorrow? Catch a movie
20.Are you easily confused? A bit ,ya
21.Do you think you would make a good parent? Ya
22.What's your favorite kind of ice cream? Any thing
24.Are you taller than 5'4"? ya
.......u missed the nos. 3,15 %26amp; 23
Reply:1.Maria
(why is there no two?)
3.both
4.sleeping in my bed
5.not really
6.nope
7.I don't know, Scream?(lol)
8.2 years ago I think
9.I hope not!
10.no, but I can make myself laugh
11.9 hours :P
12.simple
13.No, everything happens for a reason
14.Green and silver
(why isn't there a 15?)
16.No lol
17. Yep!
18.nope
19.sleeping!
20.Yes, but I can just as easily figure things out(mostly)
21.I don't know
22.I have to many favorites.
(no 23!)
24. Yep
Reply:1. andrie
2. my mummy
3. watching tv on the couch before i go to bed
4. no
5. no idea but i need to pick something cause im going to a xmas party :)
6. all of them
7. the last relationship i had that ended was almost 6 years ago. at the moment im engaged :)
8. not that i know of
9. no
10. 8 hours sleep
11. both
12. no
13. pastel pink and pastel green
14. no
15. yes
16. yes
17. going to my sister in laws for xmas day
18. no
19. i already am a parent and i think im pretty good :)
20. toffee chip
21. no im 5'2
Reply:rose
what happened to two
dad..my mom is a mean person
in bed having my husband rub my hiney so I can go to sleep
yes
work out apparel
jeffrey dahmer
20 years ago
nope
nope
7
complicated
definetly I would go back to the day my son died and lock him in the
Reply:Anne
Mom
Hopefully in bed. But I might still be awake at 1AM
Um... I don't know
Yes
Um...
Haven't had one yet
Yes, My neighbor does. It's kind of creepy.
Yes
9
Complicated
Yes
Grey, Black, Dark Green
No
No
Don't drink (underage)
Going to church
Sometimes
I like to think so
Double chocolate moose tracks
4'10"
Reply:1.) too private sorry
2.) you forgot number 2
3.) dad
4.)in bed
5.) hmmm dunno
6.) nope
7.)that clown guy
8.) a long time ago
9.) I hope not
10.) no
11.)like 6
12.) complicated
13.) whoa yeah
14.) dark colors like purple, navy blue, forest green
15.) you forgot number 15
16.) no
17.) yes
18.) no
19.) same thing I did today
20.) uuuuhhhhh can you repeat the question
21.) no
22.) gosh there are so many mint chocolate chip, cake batter, butter pecan.
23.) you forgot 23
24.) yes
3. Would you rather spend a whole day with your mom or your dad?
4.Where will you be 12 hours from now?
5.Is it easy for others to make you feel awkward?
6.Do you know what you are going to wear tomorrow?
7.What serial killer do you find most disturbing?
8.When did your last relationship end?
9.Does anyone hate you for no reason?
10.Can you make yourself cry?
11.How many hours of sleep did you get last night?
12.Is your life simple or complicated?
13.Would you go back in time if you were given the chance?
14.What are your favorite colors?
16.Do you know anyone who lives in Wyoming?
17.Have you ever kissed someone whose name starts with a C?
18.Have you ever passed out from drinking too much?
19.What are you doing tomorrow?
20.Are you easily confused?
21.Do you think you would make a good parent?
22.What's your favorite kind of ice cream?
24.Are you taller than 5'4"?
Survey: Just Random stuff.?
1. Paul, the name that i use on here (Jeff is my first name)
3. my dad- I get along better with him
4.I'll probably be at my brother's
5. Yes
6. Haha, I won't know till tomorrow gets here.
7. Definitely, Jeffrey Dahmer. One of my friends did a powerpoint presentation on him, what I learned was absolutely disturbing
8. I broke up with my last ex a year ago, and have taken time to myself since then.
9.I'm sure there are people that don't like me, but I can't think of anyone who hates me.
10. Yes, I did theater, so I know how to do that.
11. 7 hours
12. Haha, I won't go there right now.
13. Yes, I would
14. blue, teal, silver, and green
16. No, I don't
17. No, my exs names start with A, B, and M
18. no, I've been drunk, but I've never passed out.
19. finishing getting ready for the holidays
20. Yes, very. When I lived with my friend in the city for 2 months, he used to draw me road maps so I wouldn't get lost, lol.
21. Honestly, no.
22. vanilla with caramel or hot fudge
24. Yes, I'm 6'0"
Have a great day and consider yourself starred! Happy holidays!
Reply:1florence
2??
3dad
4my best friends house
5very much so
6yes
7idk of any serial killers off the top of my head...
8never had one XD
9oh yes
10yup
11 11 hours =D
12complicated
13yes
14blue
15??
16nope
17nah
18no
19party!
20yes
21yep
22moose tracks =)
23?
24no, im 5'1"
Reply:1.
3.both
4.still in my house
5.not really
6.nope
7.Albert Fish
8.a year ago
9.some people do
10.nope
11.9hrs
12.complicated
13.yes
14.purple,lime green,black,turquoise
16.no
17.no
18.i don't drink
19.sleep,wrap presents,shop,eat
20.no
21.maybe
22.strawberry
24.yes
Reply:Bliss
Neither, they are both dead.
I don't know, I haven't got there yet.
No
No
None
1972
No
Yes
9
Simple
No
Blue and Grey
Yes
Yes
Yes
Won't know untill then
No
No
Soft
Yes
Reply:1.What's your middle name? I dont have one
3. Would you rather spend a whole day with your mom or your dad? DAD!!
4.Where will you be 12 hours from now? hmmm....idk
5.Is it easy for others to make you feel awkward? Kind of
6.Do you know what you are going to wear tomorrow? NO
7.What serial killer do you find most disturbing?All of them
8.When did your last relationship end? Never had one
9.Does anyone hate you for no reason? Ya!my french teacher hates me to death and i never said or did any thing 2 her!!
10.Can you make yourself cry? Ya,jus think of my life!
11.How many hours of sleep did you get last night? 51/2
12.Is your life simple or complicated?CoMpLiCaTeD
13.Would you go back in time if you were given the chance? Ya defante
14.What are your favorite colors?Blue and green
16.Do you know anyone who lives in Wyoming? Hmmm...NO
17.Have you ever kissed someone whose name starts with a C? I kiss anyone but my mom,dad,close friends,cousins
18.Have you ever passed out from drinking too much? I have no bad habits.
19.What are you doing tomorrow? Catch a movie
20.Are you easily confused? A bit ,ya
21.Do you think you would make a good parent? Ya
22.What's your favorite kind of ice cream? Any thing
24.Are you taller than 5'4"? ya
.......u missed the nos. 3,15 %26amp; 23
Reply:1.Maria
(why is there no two?)
3.both
4.sleeping in my bed
5.not really
6.nope
7.I don't know, Scream?(lol)
8.2 years ago I think
9.I hope not!
10.no, but I can make myself laugh
11.9 hours :P
12.simple
13.No, everything happens for a reason
14.Green and silver
(why isn't there a 15?)
16.No lol
17. Yep!
18.nope
19.sleeping!
20.Yes, but I can just as easily figure things out(mostly)
21.I don't know
22.I have to many favorites.
(no 23!)
24. Yep
Reply:1. andrie
2. my mummy
3. watching tv on the couch before i go to bed
4. no
5. no idea but i need to pick something cause im going to a xmas party :)
6. all of them
7. the last relationship i had that ended was almost 6 years ago. at the moment im engaged :)
8. not that i know of
9. no
10. 8 hours sleep
11. both
12. no
13. pastel pink and pastel green
14. no
15. yes
16. yes
17. going to my sister in laws for xmas day
18. no
19. i already am a parent and i think im pretty good :)
20. toffee chip
21. no im 5'2
Reply:rose
what happened to two
dad..my mom is a mean person
in bed having my husband rub my hiney so I can go to sleep
yes
work out apparel
jeffrey dahmer
20 years ago
nope
nope
7
complicated
definetly I would go back to the day my son died and lock him in the
Reply:Anne
Mom
Hopefully in bed. But I might still be awake at 1AM
Um... I don't know
Yes
Um...
Haven't had one yet
Yes, My neighbor does. It's kind of creepy.
Yes
9
Complicated
Yes
Grey, Black, Dark Green
No
No
Don't drink (underage)
Going to church
Sometimes
I like to think so
Double chocolate moose tracks
4'10"
Reply:1.) too private sorry
2.) you forgot number 2
3.) dad
4.)in bed
5.) hmmm dunno
6.) nope
7.)that clown guy
8.) a long time ago
9.) I hope not
10.) no
11.)like 6
12.) complicated
13.) whoa yeah
14.) dark colors like purple, navy blue, forest green
15.) you forgot number 15
16.) no
17.) yes
18.) no
19.) same thing I did today
20.) uuuuhhhhh can you repeat the question
21.) no
22.) gosh there are so many mint chocolate chip, cake batter, butter pecan.
23.) you forgot 23
24.) yes
(P=.30) Random Sample (n=100 families) What is Probability that sample portion is between (.20) & (.40)?
A) .0146
B) .0292
C) .4854
D) .9708
E) None of above
(P=.30) Random Sample (n=100 families) What is Probability that sample portion is between (.20) %26amp; (.40)?
First, convert each p^ (sample proportion) value to a z value using
z = (p^ - p)/s,
where s is the standard deviation for the sampling distribution of p^, which can be found using
s = sqrt(pq/n),
where q = 1-p = 1-.30 = .70.
You get s = 0.045825757 (approximately)
Your first p^ value to convert is .20:
z = (.20 - .30)/0.045825757 = -2.18
Your second p^ value to convert is .40:
z = (.40 - .30)/0.045825757 = 2.18.
I can't do the rest right now, because I don't have a chart to look up these z values. Unless you are doing this exclusively with a calculator, you shoud have a chart where you can look up the values for these z's. Look them up and subtract them to get your final answer.
EDIT: If it's not E, then it has to be D. The Empirical rule says that about 95% of the values are within two standard deviations of the mean in a normal distribution (your p^ distribution is normal because the sample size is large enough: both np = 100(.30) = 30 and nq = 100(.70) = 70 are greater than 5). Your p^ values are 2.18 standard deviations away from the mean (because that's what z says: the number of standard devations you are away from the mean). So that answer has to be more than 95%.
B) .0292
C) .4854
D) .9708
E) None of above
(P=.30) Random Sample (n=100 families) What is Probability that sample portion is between (.20) %26amp; (.40)?
First, convert each p^ (sample proportion) value to a z value using
z = (p^ - p)/s,
where s is the standard deviation for the sampling distribution of p^, which can be found using
s = sqrt(pq/n),
where q = 1-p = 1-.30 = .70.
You get s = 0.045825757 (approximately)
Your first p^ value to convert is .20:
z = (.20 - .30)/0.045825757 = -2.18
Your second p^ value to convert is .40:
z = (.40 - .30)/0.045825757 = 2.18.
I can't do the rest right now, because I don't have a chart to look up these z values. Unless you are doing this exclusively with a calculator, you shoud have a chart where you can look up the values for these z's. Look them up and subtract them to get your final answer.
EDIT: If it's not E, then it has to be D. The Empirical rule says that about 95% of the values are within two standard deviations of the mean in a normal distribution (your p^ distribution is normal because the sample size is large enough: both np = 100(.30) = 30 and nq = 100(.70) = 70 are greater than 5). Your p^ values are 2.18 standard deviations away from the mean (because that's what z says: the number of standard devations you are away from the mean). So that answer has to be more than 95%.
Just a random question.. what color[s] do you think i should dye my hair?
here are some pictures of me...
http://i18.tinypic.com/7y6y1d2.jpg
http://i19.tinypic.com/73o2zjc.jpg
http://i12.tinypic.com/71fqcs6.jpg
http://i11.tinypic.com/6ldq00p.jpg
i think about anything
so please give me ideas.
c:
Just a random question.. what color[s] do you think i should dye my hair?
i reli like your hair the way it is, but if u want a change the maybe like brown hightlights
Reply:I like it the way it is but a brunnette would look cute
Reply:a lighter blonde
Reply:if i could see your face then i could tell you what colors would look good.but speaking i cant im at a loss.sorry
Reply:u can barely see u and also we need to see ur face. I like the color now but how about red like a copper red thats always a pretty color but u have to be careful cause it makes ur pink skin tones more noticeable. or maybe a dark chocolate brown like Nikki Hilton..
Reply:Yea maybe if I saw your face it would be easier. I like what you have now but if you want to change I say light blond with some ONE funky highlight (like Blue, Pink, white, Green, etc.)
survey results
http://i18.tinypic.com/7y6y1d2.jpg
http://i19.tinypic.com/73o2zjc.jpg
http://i12.tinypic.com/71fqcs6.jpg
http://i11.tinypic.com/6ldq00p.jpg
i think about anything
so please give me ideas.
c:
Just a random question.. what color[s] do you think i should dye my hair?
i reli like your hair the way it is, but if u want a change the maybe like brown hightlights
Reply:I like it the way it is but a brunnette would look cute
Reply:a lighter blonde
Reply:if i could see your face then i could tell you what colors would look good.but speaking i cant im at a loss.sorry
Reply:u can barely see u and also we need to see ur face. I like the color now but how about red like a copper red thats always a pretty color but u have to be careful cause it makes ur pink skin tones more noticeable. or maybe a dark chocolate brown like Nikki Hilton..
Reply:Yea maybe if I saw your face it would be easier. I like what you have now but if you want to change I say light blond with some ONE funky highlight (like Blue, Pink, white, Green, etc.)
survey results
SOME MORE 'RANDOM' Qs ....?
(plz copy %26amp; paste)
1.what country are you currently in, and what time and day is it there?
2.what do you think is the most interesting section on Y/A?
3.what are the three users you admire most and the three who are most famous?
4.what other websites do you go to frequently?
5.what was your favorite grade/year in school?
6.what was the worst/best thing that happened globally and to you in the past 5 years?
7. what would you rather do?
a. listen/play music
b.watch a movie
c.read/write
d. internet/TV
8. i wish _________because __________but ________??
9. what do you wish you could do over ( i know its a learning experience and stuff, but still...)?
10. given the choice, what would you like to do for and to the world?
SOME MORE 'RANDOM' Qs ....?
1.what country are you currently in, and what time and day is it there?I live in USA It's 11:05AM sun.
2.what do you think is the most interesting section on Y/A?
P%26amp;S BABY!!
3.what are the three users you admire most and the three who are most most and the three who are most famous?
I can't choose 3
I love all of my fans
4.what other websites do you go to frequently?
Youtube
5.what was your favorite grade/year in school?
8th
6.what was the worst/best thing that happened globally and to you in the past 5 years?
I'm not sure
7. what would you rather do?
d. internet/TV
or surf
8. i wish surfing right now because I love it but maybe tommarrow I will
9. what do you wish you could do over ( i know its a learning experience and stuff, but still...)?nothing at the moment....
10. given the choice, what would you like to do for and to the world?Find a cure for something
Reply:1.what country are you currently in, and what time and day is it there? Sunday 11:10 pm
2.what do you think is the most interesting section on Y/A? : Polls and Surveys
3.what are the three users you admire most and the three who are most famous?
4.what other websites do you go to frequently?: www.myjellybean.com
5.what was your favorite grade/year in school?: 10th grade. I loved it
6.what was the worst/best thing that happened globally and to you in the past 5 years? not telling
7. what would you rather do?
a. listen/play music
b.watch a movie
c.read/write
d. internet/TV
(b)
8. i wish i could fly because i like to fly but darn i cannot fly.
9. what do you wish you could do over ( i know its a learning experience and stuff, but still...)? fall in love
10. given the choice, what would you like to do for and to the world? eradicate poverty
Reply:1. North America, its 12:09am
2.Singles/Relationships
3. I can't say.
4. Myspace.com, Photobucket.com, Hotmail.com, Youtube.com, Yahoo!.com
5.9th,6th,%26amp; Kindergarten
6. Family moving to a different part of Texas. Missing friends.
7. A/D. %26amp; sleep
8. I wish i was with him again, because i love him dearly, but i can't have him cuz he doesn't want me back.
9. Kiss the guy i love %26amp; be with him over %26amp; over again..%26amp; play with my best dog.
10. Let gay people be protected from HATE. %26amp; Not let hate be in the world today.
Reply:USA - 9:05
this one
jake wears prada/wings of vanity and wax/val
bored.com/band websites,imdb
6th grade and 4th grade
learning a lot about life and how to live in it
A
my boyfriend didnt cheat - i loved him - he did it anyways. oh well
picking who i hung out with
let it go by as i watch from afar with my love
1.what country are you currently in, and what time and day is it there?
2.what do you think is the most interesting section on Y/A?
3.what are the three users you admire most and the three who are most famous?
4.what other websites do you go to frequently?
5.what was your favorite grade/year in school?
6.what was the worst/best thing that happened globally and to you in the past 5 years?
7. what would you rather do?
a. listen/play music
b.watch a movie
c.read/write
d. internet/TV
8. i wish _________because __________but ________??
9. what do you wish you could do over ( i know its a learning experience and stuff, but still...)?
10. given the choice, what would you like to do for and to the world?
SOME MORE 'RANDOM' Qs ....?
1.what country are you currently in, and what time and day is it there?I live in USA It's 11:05AM sun.
2.what do you think is the most interesting section on Y/A?
P%26amp;S BABY!!
3.what are the three users you admire most and the three who are most most and the three who are most famous?
I can't choose 3
I love all of my fans
4.what other websites do you go to frequently?
Youtube
5.what was your favorite grade/year in school?
8th
6.what was the worst/best thing that happened globally and to you in the past 5 years?
I'm not sure
7. what would you rather do?
d. internet/TV
or surf
8. i wish surfing right now because I love it but maybe tommarrow I will
9. what do you wish you could do over ( i know its a learning experience and stuff, but still...)?nothing at the moment....
10. given the choice, what would you like to do for and to the world?Find a cure for something
Reply:1.what country are you currently in, and what time and day is it there? Sunday 11:10 pm
2.what do you think is the most interesting section on Y/A? : Polls and Surveys
3.what are the three users you admire most and the three who are most famous?
4.what other websites do you go to frequently?: www.myjellybean.com
5.what was your favorite grade/year in school?: 10th grade. I loved it
6.what was the worst/best thing that happened globally and to you in the past 5 years? not telling
7. what would you rather do?
a. listen/play music
b.watch a movie
c.read/write
d. internet/TV
(b)
8. i wish i could fly because i like to fly but darn i cannot fly.
9. what do you wish you could do over ( i know its a learning experience and stuff, but still...)? fall in love
10. given the choice, what would you like to do for and to the world? eradicate poverty
Reply:1. North America, its 12:09am
2.Singles/Relationships
3. I can't say.
4. Myspace.com, Photobucket.com, Hotmail.com, Youtube.com, Yahoo!.com
5.9th,6th,%26amp; Kindergarten
6. Family moving to a different part of Texas. Missing friends.
7. A/D. %26amp; sleep
8. I wish i was with him again, because i love him dearly, but i can't have him cuz he doesn't want me back.
9. Kiss the guy i love %26amp; be with him over %26amp; over again..%26amp; play with my best dog.
10. Let gay people be protected from HATE. %26amp; Not let hate be in the world today.
Reply:USA - 9:05
this one
jake wears prada/wings of vanity and wax/val
bored.com/band websites,imdb
6th grade and 4th grade
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The following random sample from a population whose values where normally distributed were collected.?
10 8 11 11
the 95% confidence interval for the mean is:
A) 8.52 to 10.98
b) 7.75 to 11.75
c) 9.75 to 10.75
d) 8 to 10
The following random sample from a population whose values where normally distributed were collected.?
I get a different answer. Surely none of these answers can be right: in no case is the interval symmetric about the mean = 10.
Sample size n = 4
Sample mean xbar = 40/4 = 10
Population mean = mu (unknown)
Sample variance s^2 = (0 + 4 + 1 + 1)/(4-1) = 2
(Note: dividing here by n-1 = 4-1 is more accurate than by n because it makes s^2 an exactly unbiased estimator of the population variance sigma^2. This would matter little if n were large.)
Std error = s/sqrt(n) = sqrt(2)/2 = 0.707
So xbar-mu is normally distributed with mean 0 and std dev 0.707 (as estimated from the sample; its exact but unknown value is sigma/sqrt(n) = sigma/2).
So the 95% confidence interval for mu is
[10 - 1.96*0.707, 10 + 1.96*0.707] = [8.614,11.386].
Remark 1: With such a small sample, you really have to take (n-1) = 3 instead of n = 4 in calculating the sample variance s^2. The formula for s^2 "mean of squares - square of mean" under-estimates sigma^2 by the factor n/(n-1) = 4/3 here. This is not inconsiderable. The unbiased estimate of s^2 from this sample is 2, and NOT 1.5 as in Wal C's solution.
Even the value s^2 = 2 will lead to under-estimating the population std dev. sigma itself (because sqrt is a concave fctn, s is an under-estimating estimator of sigma even though s^2 is an unbiased estimator of sigma^2).
Remark 2: Wal C's solution is even more seriously wrong. She should have used the std error, the std dev of the sample mean, which is sigma/sqrt(n). But she used the std dev. of a SINGLE trial, sigma. If that were correct, there would never be any point in increasing the sample size! The point is of course that the std error sigma/sqrt(n) goes down as n increases -- but you've got to use this fact, not ignore it!
Remark 3: My solution above is also faulty. The sample size is so small that you must use the Student t-distribution and not the normal distribution. (xbar-mu)/(s/sqrt(n)) is not normally distributed; it has the Student t-distribution with 4-1=3 degrees of freedom. The 97.5 percentile is 3.18 (and not 1.96 as for the normal distr), and so the 95% confidence interval for mu is
[10 - 3.18*0.707, 10 + 3.18*0.707] = [7.75, 12.25].
Reply:10 8 11 11
Mean = 40/4 = 10
Mean of squares = 406/4 = 101.5
Variance = Mean of squares - square of mean
= 101.5 - 100
= 1.5
So SD = σ = √1.5 ≈ 1.22
2σ = 2.45
95% Interval ≈ μ ± 2σ
ie from 10 - 2 x 1.225 to 10 + 2 x 1.225
ie 7.55 to 12.45
So none of them is correct
The 68% confidence interval is approximately μ ± σ
ie 8.775 to 11.225 so none of them are correct on this figure either.
And if you take into account that this is a small sample then the sample SD = √(4/3) * 1.225 ≈ 1.41 then the 68% interval grows to around 8.59 to 11.41 and the 95% interval to around 7.18 to 12.82
the 95% confidence interval for the mean is:
A) 8.52 to 10.98
b) 7.75 to 11.75
c) 9.75 to 10.75
d) 8 to 10
The following random sample from a population whose values where normally distributed were collected.?
I get a different answer. Surely none of these answers can be right: in no case is the interval symmetric about the mean = 10.
Sample size n = 4
Sample mean xbar = 40/4 = 10
Population mean = mu (unknown)
Sample variance s^2 = (0 + 4 + 1 + 1)/(4-1) = 2
(Note: dividing here by n-1 = 4-1 is more accurate than by n because it makes s^2 an exactly unbiased estimator of the population variance sigma^2. This would matter little if n were large.)
Std error = s/sqrt(n) = sqrt(2)/2 = 0.707
So xbar-mu is normally distributed with mean 0 and std dev 0.707 (as estimated from the sample; its exact but unknown value is sigma/sqrt(n) = sigma/2).
So the 95% confidence interval for mu is
[10 - 1.96*0.707, 10 + 1.96*0.707] = [8.614,11.386].
Remark 1: With such a small sample, you really have to take (n-1) = 3 instead of n = 4 in calculating the sample variance s^2. The formula for s^2 "mean of squares - square of mean" under-estimates sigma^2 by the factor n/(n-1) = 4/3 here. This is not inconsiderable. The unbiased estimate of s^2 from this sample is 2, and NOT 1.5 as in Wal C's solution.
Even the value s^2 = 2 will lead to under-estimating the population std dev. sigma itself (because sqrt is a concave fctn, s is an under-estimating estimator of sigma even though s^2 is an unbiased estimator of sigma^2).
Remark 2: Wal C's solution is even more seriously wrong. She should have used the std error, the std dev of the sample mean, which is sigma/sqrt(n). But she used the std dev. of a SINGLE trial, sigma. If that were correct, there would never be any point in increasing the sample size! The point is of course that the std error sigma/sqrt(n) goes down as n increases -- but you've got to use this fact, not ignore it!
Remark 3: My solution above is also faulty. The sample size is so small that you must use the Student t-distribution and not the normal distribution. (xbar-mu)/(s/sqrt(n)) is not normally distributed; it has the Student t-distribution with 4-1=3 degrees of freedom. The 97.5 percentile is 3.18 (and not 1.96 as for the normal distr), and so the 95% confidence interval for mu is
[10 - 3.18*0.707, 10 + 3.18*0.707] = [7.75, 12.25].
Reply:10 8 11 11
Mean = 40/4 = 10
Mean of squares = 406/4 = 101.5
Variance = Mean of squares - square of mean
= 101.5 - 100
= 1.5
So SD = σ = √1.5 ≈ 1.22
2σ = 2.45
95% Interval ≈ μ ± 2σ
ie from 10 - 2 x 1.225 to 10 + 2 x 1.225
ie 7.55 to 12.45
So none of them is correct
The 68% confidence interval is approximately μ ± σ
ie 8.775 to 11.225 so none of them are correct on this figure either.
And if you take into account that this is a small sample then the sample SD = √(4/3) * 1.225 ≈ 1.41 then the 68% interval grows to around 8.59 to 11.41 and the 95% interval to around 7.18 to 12.82
Jointly Distributed random variables?
annie and alvie have agreed to meet between 5pm and 6pm for dinner at a health food restaurant. x=annies arival time, y=alvies arrival time. x and y are independent with each uniformly distributed on the interval [5,6].
a) whats the joint pdf of x and y?
b)whats the probability they both arrive between 5:15 and 5:45?
c) if the first one to arrive with only wait 10 min before leaving, whats the probability that they have dinner at the health food restaurant? [hint: the event of interest is A={(x,y): |x-y|%26lt;=1/6}.]
Jointly Distributed random variables?
a) the pdf for a uniform distribution over an interval [a,b] is
f(x) = 1/(b-a) = 1 in your case since 6-5=1.
Siince they are both independent then the joint pdf is the product of the 2 pdf s . Each pdf is 1 over the whole inerval so the joint pdf g(x) is also 1*1 = 1 for all x in [5,6] and 0 otherwise.
b) looks good.
c) the area in question is bounded by the area: x-1/2 %26lt; y and y%26lt; x + 1/6. This will give you teh complement of what you calculated. Ans I have is .30555 (that's 1 - your answer) which makes more sense than the bigger probability you have. To make things simple, use the interval [0,1] to draw your lines instead of [5,6]. The correct area is the small diagonal rectangle plus the two little triangles next to it (coordinates (0,1/6), (1/6,0), (0,0), and (1,1), (5/6,1) , (1,5/6)
a) whats the joint pdf of x and y?
b)whats the probability they both arrive between 5:15 and 5:45?
c) if the first one to arrive with only wait 10 min before leaving, whats the probability that they have dinner at the health food restaurant? [hint: the event of interest is A={(x,y): |x-y|%26lt;=1/6}.]
Jointly Distributed random variables?
a) the pdf for a uniform distribution over an interval [a,b] is
f(x) = 1/(b-a) = 1 in your case since 6-5=1.
Siince they are both independent then the joint pdf is the product of the 2 pdf s . Each pdf is 1 over the whole inerval so the joint pdf g(x) is also 1*1 = 1 for all x in [5,6] and 0 otherwise.
b) looks good.
c) the area in question is bounded by the area: x-1/2 %26lt; y and y%26lt; x + 1/6. This will give you teh complement of what you calculated. Ans I have is .30555 (that's 1 - your answer) which makes more sense than the bigger probability you have. To make things simple, use the interval [0,1] to draw your lines instead of [5,6]. The correct area is the small diagonal rectangle plus the two little triangles next to it (coordinates (0,1/6), (1/6,0), (0,0), and (1,1), (5/6,1) , (1,5/6)
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