To check whether there is a reason to believe that the average height has been changed, we can check one right-tailed test and establish null and alternate hypotheses.
H₀ (null hypothesis): μ = 162.5
H₁ (alternate hypothesis): μ > 162.5
Since we have two samples to compare, we can use the formula below to compute for the z-score.
where Z is the z-score, Χ is the new mean of the sample, μ is the expected average value, δ is the standard deviation, and n is the sample size. Given the values we have,
Assuming that the significance level, α, is 0.05. Now that we have a z-score of 2.77, we can use the z-table to find its p-value. Thus, we have P(Z > 2.77) = .0028. Thus since our p-value is less than α, H₀ is rejected. That means that the average height of the female freshman students has changed.
H₀ (null hypothesis): μ = 162.5
H₁ (alternate hypothesis): μ > 162.5
Since we have two samples to compare, we can use the formula below to compute for the z-score.
where Z is the z-score, Χ is the new mean of the sample, μ is the expected average value, δ is the standard deviation, and n is the sample size. Given the values we have,
Assuming that the significance level, α, is 0.05. Now that we have a z-score of 2.77, we can use the z-table to find its p-value. Thus, we have P(Z > 2.77) = .0028. Thus since our p-value is less than α, H₀ is rejected. That means that the average height of the female freshman students has changed.