Question

The average height of men in 1960 was found to be 68 inches (5 feet, 8 inches). A researcher claims that men today are taller than they were in 1960 and would like to test this hypothesis at the 0.01 significance level. The researcher randomly selects 9797 men and records their height to find an average of 69.702069.7020 inches with standard deviation of 2.0024 inches.

Step 1 of 2:

What is the value of the test statistic? Round your answer to four decimal places.

Step 2 of 2:

What is your decision regarding the null hypothesis?

a. Fail to reject the null hypothesis. At the 1% significance level there is not sufficient evidence to say that men today are taller than they were in 1960

B. Reject the null hypothesis. At the 1% significance level there is not sufficient evidence to say that men today are taller than they were in 1960.

c. Fail to reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

d. Reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

Answer #1

Below are the null and alternative Hypothesis,

Null Hypothesis: μ = 68

Alternative Hypothesis: μ > 68

Rejection Region

This is right tailed test, for α = 0.01 and df = 96

Critical value of t is 2.366.

Hence reject H0 if t > 2.366

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (69.702 - 68)/(2.0024/sqrt(97))

t = 8.371

P-value Approach

P-value = 0.0000

As P-value < 0.01, reject the null hypothesis.

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