Question

Please help,

Answer 1

Carla wants to determine if there is a difference in the mean body temperature between men and women. She knows that mean body temperature for a sample of 100 men is 97.1 with a population standard deviation of 0.51 and the mean body temperature for a sample of 100 women is 98.2 with a population standard deviation of 0.57.

Answer 2

Assuming the population of body temperatures for men and women is normally distributed, calculate the 95% 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 3

what part are we having an issue with?

Answer 4

a confidence interval tells us to what degree of assuredness that the true population parameter is contained somewhere within the interval basing the assumption off of the normal distribution of sample means

Answer 5

so how would I calculate 95% confidence interval?

Answer 6

this might help
http://www.dummies.com/how-to/content/how-to-calculate-a-confidence-interval-for-a-popul.navId-811046.html

Answer 7

if you can determine a z score, a confidence interval is pretty much the same thing

Answer 8

\[z=\frac{x-mean}{sd/\sqrt{n}}\]
\[z(sd/\sqrt{n})=x-mean\]
\[mean\pm z(sd/\sqrt{n})=\pm x=CI\]

Answer 9

the key is interpreting the z score related to the percentage. if we are tabled from the mean, then its related to just half the percentage; otherwise we adjust it for a tailed table as needed by adding half remaining probability to it

Answer 10

we could just as well table half the remaining probability since a normal distribution is symmetric

Answer 11

left tail to find a z score related to (1-.95)/2 = .05/2 = .0250

Answer 12

and how do i find the mean?

Answer 13

the mean is found by reading it directly from the information that was given

Answer 14

since the sample mean of men is 97.1, as stated in the problem ... i would simply use that

Answer 15

@phi i figured out the margin of error and the questions asks to explain what the confidence intervals mean in the context of the problem, how do i do that exactly?

Answer 16

out of curiosity, what did you get for the CI for men ?

Answer 17

well i used to confidence interval of 95%

Answer 18

which is 1.96

Answer 19

that is good, but it's only the the path to the final answer.

Answer 20

you use 1.96 * sigma/sqrt(# of samples) to find the CI

for men: 1.96 * 0.51 /sqr(100)

Answer 21

yeah i calculated that out already and got 0.09996, but my question is, what do they mean by "explain what the confidence intervals mean in the context of the problem"

Answer 22

ok, just checking. It would be a shame to not get the first part correct.

The confidence interval means that if you perform the survey many times, and find the confidence interval, 95% of the these surveys will have a confidence interval that contains the "true population mean"

Answer 23

okay thank you

Answer 24

so how would i word my answer to that question exactly?

Answer 25

good question. The margin of error for men is about 0.1, so the confidence interval is very tight. If you perform lots of surveys (with this very tight interval), 95% of them will contain the true population mean, so we would expect it to be very close to 97.1 that we see in this one survey.

Answer 26

:o Thankyou so much @phi This was really well explained ^-*