Question

A statistician wishes to test the claim that the average weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 35 firemen and found s = 27.2 pounds.

Assuming that the weights of the firemen are normally distributed, if the statistician wanted to test her research hypothesis at the .05 level of significance, what is the critical value?

Place your answer, rounded to 3 decimal places, in the blank. For example, 23.456 would be a legitimate entry.

Correct Answer is 1.645, my answer came 1.691

Can some one please show the calculations of the right answer and explain why my answer was slightly off?

Answer 1

Let X be the weight of a fireman(in pounds).

Given n=35 and s=27.2 pounds.

At 5% level of significance we want to test the claim that the average weights of firemen is greater than 25 pounds.

Since the sample size is n=35, the degrees of freedom for the test is df=n-1=34

Hence z critical value for upper tail test is:

### Since the sample size is greater than 30, we used z test for the test of significance of population mean.

### By using excel function: =NORMINV(0.95,0,1)

Hence,