Question

A study by a researcher in a lab is to address the question of whether the mean body temperature of humans is 37°C. The body temperatures of six graduate students in the lab were measured (35.5, 36, 37.5, 35, 36.5, 37.8). Note that the sample mean is = 36.383. Assume that the standard deviation of the body temperatures of humans is 0.5°C.

a) Test at the 5% significance level whether the average body temperature of humans is different from 37°C. Complete all 6 steps of your hypothesis test, including a discussion of the assumptions.

Answer 1

To test whether the average human body temperature is different from 37°C, a hypothesis test at the 5% significance level is performed, involving stating the null and alternative hypotheses, calculating the test statistic, and comparing it with the critical z-value to make a decision.

Step-by-step explanation:

Hypothesis Testing for Mean Body Temperature

To determine whether the mean body temperature is different from 37°C, a hypothesis test at the 5% significance level can be used. The null hypothesis (​H​​0​​) is that the mean body temperature is 37°C, while the alternative hypothesis (​H​​1​​) is that the mean is different from 37°C.

Here are the steps for the hypothesis test:

1. 
   
3. State the hypotheses: ​H​​0​​: μmu = 37, ​H​​1​​: μmu ≠ 37.
4. 
   
6. Choose the significance level (α)​: 0.05 in this case.
7. 
   
9. Calculate the test statistic using the formula z = (x​​​​8 - μmu)/(sigma/√n), where x​​​​8 is the sample mean, μmu is the population mean, sigma is the population standard deviation, and n is the sample size.
10. 
    
12. Determine the critical z-value from the z-table corresponding to the 5% significance level.
13. 
    
15. Compare the test statistic to the critical value. If the test statistic lies outside the range set by the critical values, reject ​H​​0.
16. 
    
18. Interpret the results in the context of the study.

>Assumptions for the test include that the sample is randomly selected and that the standard deviation given is a good estimate of the population standard deviation. Also, the central limit theorem supports using the z-distribution when the sample size is small and the population standard deviation is known.