Question

Consider the following hypotheses: H0: μ ≤ 76.7 HA: μ > 76.7 A sample of 41 observations yields a sample mean of 78.0. Assume that the sample is drawn from a normal population with a population standard deviation of 4.4. (You may find it useful to reference the appropriate table: z table or t table) a-1. Find the p-value. 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 a-2. What is the conclusion if α = 0.10? Do not reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is greater than α. Reject H0 since the p-value is smaller than α. Reject H0 since the p-value is greater than α. a-3. Interpret the results at α = 0.10. We cannot conclude that the sample mean is greater than 76.7. We conclude that the sample mean is greater than 76.7. We cannot conclude that the population mean is greater than 76.7. We conclude that the population mean is greater than 76.7. b-1. Calculate the p-value if the above sample mean was based on a sample of 148 observations. p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 b-2. What is the conclusion if α = 0.10? Reject H0 since the p-value is smaller than α. Reject H0 since the p-value is greater than α. Do not reject H0 since the p-value is smaller than α. Do not reject H0 since the p-value is greater than α. b-3. Interpret the results at α = 0.10. We conclude that the sample mean is greater than 76.7. We cannot conclude that the sample mean is greater than 76.7. We conclude that the population mean is greater than 76.7. We cannot conclude that the population mean is greater than 76.7.

Answer 1

a-1)

0.025 p-value < 0.05

a-2)Reject H0 since the p-value is smaller than α.

a-3) . We conclude that the population mean is greater than 76.7.

b-1) p-value < 0.01

b-2)Reject H0 since the p-value is smaller than α.

b-3) . We conclude that the population mean is greater than 76.7.