Question

You wish to test the following claim ( H a ) at a significance level of α = 0.005 .

H o : μ = 60.5 H a : μ ≠ 60.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 17 with mean ¯ x = 52.3 and a standard deviation of s = 10.6

What is the test statistic for this sample? test statistic = Round to 3 decimal places

What is the p-value for this sample? p-value = Use Technology Round to 4 decimal places.

The p-value is...

a) less than (or equal to)

b) α greater than α

This test statistic leads to a decision to...

a) reject the null

b) accept the null

c) fail to reject the null

As such, the final conclusion is that...

a) There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 60.5.

b) There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 60.5.

c) The sample data support the claim that the population mean is not equal to 60.5.

d) There is not sufficient sample evidence to support the claim that the population mean is not equal to 60.5

I don't understand how to get the p value. Can you please break it down when it comes to the p value and how you arrived at the answer.

Thank You

Answer 1

Test Statistic :-

t = -3.1896

Test Criteria :-

Reject null hypothesis if

Result :- Fail to reject null hypothesis

Conclusion :- Accept Null Hypothesis

μ = 60.5

P value

Looking for value | t | = 3.1896 in t table across 16 degree of freedom

| t | = 3.1896 lies between the value 2.921 and 3.686 with respective P value are 0.01 and 0.002

Using excel to calculate exact P value = 0.00570

Reject null hypothesis if P value <  α = 0.005

0.0570 > 0.005, we fail to reject null hypothesis

The p-value is...

b) α greater than α

This test statistic leads to a decision to...

c) fail to reject the null

the final conclusion is that...

d) There is not sufficient sample evidence to support the claim that the population mean is not equal to 60.5