Question

Carl conducted an experiment to determine if there is a difference in the mean body temperature between men and women. He found that the mean body temperature for a sample of 100 men was 91.1 with a population standard deviation of 0.52 and the mean body temperature for a sample of 100 women was 97.6 with a population standard deviation of 0.45.

Answer 1

Assuming the population of body temperatures for men and women is normally distributed, calculate the 98% confidence interval and the margin of error for the mean body temperature for both men and women. Using complete sentences, explain what these confidence intervals mean in the context of the problem.

Answer 2

@rational

Answer 3

@ganeshie8

Answer 4

I know the confidence interval at 98% is 2.33 but that's about it.

Answer 5

good, start by finding standard error :
\[\text{standard error}=\dfrac{\text{standard deviatoin}}{\sqrt{\text{sample size}}}\]

Answer 6

Men :
`He found that the mean body temperature for a sample of 100 men was 91.1 with a population standard deviation of 0.52 `
\[\text{standard error}=\dfrac{\text{0.52}}{\sqrt{\text{100}}}=0.052\]
\[\text{margin of error} = \color{blue}{2.33}\times 0.052 = 0.12116\approx 0.12\]
\[\text{confidence interval} : (91.1-0.12,~91.1+0.12)=(90.98,~91.22)\]

Answer 7

see if you can find the confidence interval for women similarly

Answer 8

take ur time:)

Answer 9

let me know if somethign is not clear n above work for men

Answer 10

what would 0.10485 simplify to?

Answer 11

0.10?

Answer 12

Yes looks good

Answer 13

0.10 is the margin of error for women is it

to get confidence interval, simply subtract and add that "margin of error" from the mean.

Answer 14

ok i got (97.5,97.7)

Answer 15

did it post? my internet is funky right now

Answer 16

Looks perfect!

Answer 17

Im gonna interrupt ....
Now what can you conclude by seeing the 2 intervals?

Answer 18

i was just about to ask about that but i would think that the range of values lies within 98%

Answer 19

Or something like that, im not sure how to explain it

Answer 20

ok well lets view it like this
The 98% confidence intervals is an interval where there is a 98% chance that the population mean lies within that interval
See its kinda impossible to test all humans to determine the mean temp for women and men so we use an unbiased sample and use that information to determine an interval where there is a 98% chance that the population mean lies within that interval

Answer 21

Within the context of this problem there is a 98% chance that the population mean for a man's body temp is (90.98, 91.22) and for a woman's body temp its (97.5,97.7)

So we can conclude that the body temps for a man and woman differ

Answer 22

thanks both of you for all your help!