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The athletic director at a large university compared the proportions of freshmen (1st year students) and...

The athletic director at a large university compared the proportions of freshmen (1st year students) and seniors (4th year students) who exercise regularly. She analyzed the data and found the Z-statistic for the difference between the population proportions to be 2.43 with a P-value of 0.015. The level of significance was set at 0.05. a. State the conclusion she can draw about the difference between the two population proportions.

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Answer: The athletic director at a large university compared the proportions of freshmen (1st year students) and seniors (4th year students) who exercise regularly. She analyzed the data and found the Z-statistic for the difference between the population proportions to be 2.43 with a P-value of 0.015. The level of significance was set at 0.05. a. State the conclusion she can draw about the difference between the two population proportions.

Solution:

Null hypothesis Ho: p1 = p2

Alternative hypothesis Ha: p1 ≠ p2

Significance level, α = 0.05

Z statistic = 2.43

P-value = 0.015

Since, P-value (0.015) < α (0.05)

We reject the null hypothesis Ho.

There is sufficient evidence to conclude that there is a difference in between population proportions.

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