Question

In a random sample of 90 students in first grade, the mean hours of sleep per night was 9.2 with a standard deviation of 0.37. In a random sample of 70 students in 12th grade, the mean hours of sleep per night was 7.3 with a standard deviation of 0.58. Which interval is 99% confidence interval for the difference between the mean hours of sleep?

Answer 1

@satellite73 @Directrix

Answer 2

don't know any statistics, sorry

Answer 3

ok thank you

Answer 4

@ganeshie8

Answer 5

@tkhunny

Answer 6

@kropot72

Answer 7

The 99% confidence interval for the difference between the mean hours of sleep is found from the following:
\[\large (\bar{x}_{1}-\bar{x}_{2})\pm2.576\sqrt{\frac{s _{1}^{2}}{n _{1}}+\frac{s _{2}^{2}}{n _{2}}}\]
where s1 is the standard deviation of the first sample and s2 is the standard deviation of the second sample.

Answer 8

yes I already did the square root part and the z part but what im missing is what is between the parenthesis and that is where im stuck

Answer 9

\[\large (\bar{x}_{1}-\bar{x}_{2})=(9.2-7.3)\]
It is the difference between the sample means.

Answer 10

alright thank you let me calculate it then

Answer 11

I think something is wrong my values don't match my options but they get close

Answer 12

I did (9.2-7.3)+2.58sqrt0.37/90+0.58/70=2.1872

Answer 13

You have not followed the formula properly. The values 0.37 and 0.58 must be squared.

Answer 14

omg yes! im sorry I forgot that thank you

Answer 15

You're welcome :)

Answer 16

how did you find the margin of error? can you explain please

Answer 17

@kropot72

Answer 18

The margin of error is found by taking half the width of the confidence interval. What was your result for the confidence interval?

Answer 19

1.97 and 1.82

Answer 20

That is not the correct confidence interval. The CI is found from:
\[\large CI=1.9\pm(2.576\times0.0795)\]

Answer 21

are you sure?

Answer 22

because that is one of the options but my answers are also a choice

Answer 23

Yes, I'm sure. What are the options?

Answer 24

(1.82, 1.98)
(1.74, 2.06
1.69, 2.11)
(1.79, 2.01)

Answer 25

Which of these options is nearest to the calculation result?

Answer 26

according to you its C but I got A

Answer 27

The reason you got A, is you have not multiplied the result of taking the square root of the sum of the two fractions by 2.576.

Answer 28

ohhh ok thank you

Answer 29

but I did it by scientific calculator

Answer 30

I also used a scientific calculator.

Answer 31

oh ok then I honestly dont understand what was the mistake :/

Answer 32

Perhaps you can repeat the calculation, but do it in steps. First calculate the value of the square root of the sum of the two fractions. Then multiply the result by 2.576. The final result should be 0.20479.

Answer 33

did you place the whole equation into the calculator or did you go step by step?

Answer 34

I get the same result from entering the whole calculation and by doing it in steps.

Answer 35

oh ok then you must be correct

Answer 36

You're welcome :)

Answer 37

btw I also have this last question if you don't mind pleasee

Answer 38

http://www.science-mathematics.com/Mathematics/201205/30650.htm

Answer 39

@kropot72

Answer 40

in my opinion the answer is There is a 95% probability that female seniors at this high school read between 3.09 and 3.31 more books per year than male seniors at this high school.

Answer 41

My calculation shows that the first statement is correct.

Answer 42

can you explain

Answer 43

oh no wait is that I just noticed that table is different from mine hold on

Answer 44

Males
n1=107
x(x-bar)1=8.4
s1=2.3

Females
n2=120
x(x-bar)2=5.9
s2=1.5

Answer 45

I used the formula that I gave you for the first question, and substituted the given values. The calculation is as shown in the image that you posted.

Answer 46

yeah im sorry is that graph was different that is why I got a different result and why I believe the answer is C

Answer 47

A is correct for the question that you posted.

Answer 48

and these are the options sorry I shouldn't have give you the website the question is off
these are the options
There is a 95% probability that female seniors at this high school read between 2.37 and 2.87 more books per year than male seniors at this high school.
There is a 95% probability that male seniors at this high school read between 1.99 and 3.01 more books per year than female seniors at this high school.
There is a 95% probability that female seniors at this high school read between 2.37 and 2.87 more books per year than male seniors at this high school.
There is a 95% probability that male seniors at this high school read between 1.99 and 3.01 more books per year than female seniors at this high school.

Answer 49

Sorry, I must log out now. Please post as a new question for someone else to help you.

Answer 50

aww is ok then I think I'll just go with what I think because no one here wants to help with statistics