Question

You wish to test the following claim ( H 1 ) at a significance level of α = 0.005 . H 0 : μ = 74.5 H 1 : μ > 74.5 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 15 with mean ¯ x = 86.8 and a standard deviation of s = 13.2 . What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 74.5. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 74.5. The sample data support the claim that the population mean is greater than 74.5. There is not sufficient sample evidence to support the claim that the population mean is greater than 74.5.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 74.5
Alternative Hypothesis: μ > 74.5

Rejection Region
This is right tailed test, for α = 0.005 and df = 14
Critical value of t is 2.977.
Hence reject H0 if t > 2.977

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (86.8 - 74.5)/(13.2/sqrt(15))
t = 3.609

P-value Approach
P-value = 0.001
As P-value < 0.005, reject the null hypothesis.

The sample data support the claim that the population mean is greater than 74.5.