Hello, I am having a difficult time coming up with the variance and standard dev

Question

Hello, I am having a difficult time coming up with the variance and standard deviation for the following problem. I know that the standard deviation is suppose to be .77, I just do not know how to come up with that number. I am hoping that you can show me in detail so that I can completely comprehend it. Thank you in advance!

A medical researcher attempted to learn if a poorly understood disease is accompanied by an increase in body temperature. She measured the body temperature of 12 people diagnosed as having the disease and obtained the following temperatures (in Fahrenheit): 99.3, 99.1, 100.4, 98.4, 98.2, 98.9, 99.7, 100.1, 100.7, 99.0, 98.8, and 99.2.

Does the mean body temparature of these individuals differ from the population mean of 98.6 Fahrenheit?

Explanation / Answer

Please see the highlighted as answer to your question.

Sample mean = 99.32

Pop. mean = 98.6

Standard deviation = .77

t = (99.32 - 98.6)/ (.77/sqrt(12)) = 3/24 at df = n-1 = 12-1 = 11

It is beyond 2.201 , the critical t value at df = 11, So, we conclude that we reject the null hypothesis.

The mean body temparature of these individuals differs from the population mean of 98.6 Fahrenheit

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