At an alpha level of 0.05, test the null hypothesis against the alternative, so

Question

At an alpha level of 0.05, test the null hypothesis against the alternative, so the mean height of randomly selected statistics students is greater than the population norm (? = 63, ? = 2.5). The random sample has size n = 36 and sample mean height = 64. Select a correct answer (requires a correct P-value and conclusion to be a correct answer): P-value = 0.008 < 0.05, reject H0 and conclude that the average student height is greater than 63. P-value = 0.016 < 0.05, reject H0 and conclude that the average student height is greater than 63. P-value = 0.984 > 0.05, do not reject H0 and conclude that the average student height is greater than 63. P-value = 0.992 > 0.05, do not reject H0 and conclude that the average student height is greater than 63.

Explanation / Answer

Test statistic = (sample mean - µ) / (sd / sqrt(n)) = (64 - 63) / (2.5 / sqrt(36)) = 2.4

P-value = P(Z > 2.4) = 1 - P(Z < 2.4) = 1 - 0.9918 = 0.0082

Option-A) P-value = 0.008 < 0.05, reject H0 and conclude that the average student height is greater than 63.

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