Question

You wish to test the following claim ( H a ) at a significance level of α = 0.02 . H o : μ = 61.5 H a : μ ≠ 61.5 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 = 75.7 and a standard deviation of s = 15.7 . 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... 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 not equal to 61.5. There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 61.5. The sample data support the claim that the population mean is not equal to 61.5. There is not sufficient sample evidence to support the claim that the population mean is not equal to 61.5.

Answer 1

We have give the information that population is normally distributed and the population standard deviation is unknown.

The null and the alternative hypothesis are:

; i.e., the population mean is not different than 61.5

; i.e., the population mean is different than 61.5

At significance level we need to test this hypothesis.

Given: sample size: , sample mean: , sample standard deviation:

Test-statistic:

Degree of freedom:

So, the test-statistic is calculated as

P-value: Since it is a two-tailed hypothesis, so the p-value for the test-statistic , with degree of freedom, is calculated as-

So, the p-value is calculated as

Decision: The significance level is given as and the p-value is calculated as

Since,

So at significance level of the sample data provides sufficient evidence to reject the null hypothesis H₀ .

In other words, "The sample data provides sufficient evidence to reject null hypothesis, hence we conclude that the population mean is not equal to 61.5 or population mean is different than 61.5"