Question

In a hypothesis test with hypotheses H 0 : μ ≤ 45 and H 1 : μ > 45 , a random sample of 69 elements selected from the population produced a mean of 47.3. Assume that σ = 7.3, and that the test is to be made at the 2.5% significance level. What is the critical value of z? -1.96 1.96 -1.65 1.65 What is the value of the test statistic, z, rounded to three decimal places? What is the p-value for this hypothesis test, rounded to four decimal places? Should you reject or fail to reject the null hypothesis in this test?

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Answer #1

The null and alternative hypothesis is ,

The test is one-tailed test.

The critical value is ,

; From Z-table

The value of the test statistic is ,

The p-value is ,

p-value=

The Excel function is , =1-NORMDIST(2.617,0,1,TRUE)

Decision : Here , p-value < 2.5%=0.025

Therefore , reject the null hypothesis.

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