Use Technology and a ttest to test the claim about the popul

Use Technology and a t-test to test the claim about the population mean u at the given level of significance a using the given sample statistics . Assume the population is normally distributed.

Claim: u>77; a=0.05 Sample statistics: x= 79.9, s=2.9 n=26

a What are the null and alternative hypotheses?

b. What is the value of the standardized test statistic?

c What is the P-value of the test statistic?

Decide whether to reject of fail to reject the null hypothesis.

Solution

a What are the null and alternative hypotheses?

Let mu be the population mean

Null hypothesis: mu=77

Alternative hypothesis: mu>77

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b. What is the value of the standardized test statistic?

The test statistic is

Z=(xbar-mu)/(s/vn)

=(79.9-77)/(2.9/sqrt(26))

=5.10

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c What is the P-value of the test statistic?

It is a right-tailed test.

So the p-value= P(Z>5.10)=0 (from standard normal table)

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Decide whether to reject of fail to reject the null hypothesis.

Since the p-value is less than 0.05, we reject the null hypothesis.