Question

Exercise 9-13 Algo

Consider the following hypotheses:

H₀: μ ≤ 73.0
H_A: μ > 73.0

A sample of 51 observations yields a sample mean of 74.3. Assume that the sample is drawn from a normal population with a population standard deviation of 3.7. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Find the p-value.
  

• 0.01 p-value < 0.025
• 0.025 p-value < 0.05
• 0.05 p-value < 0.10
• p-value 0.10

• p-value < 0.01

a-2. What is the conclusion if α = 0.01?
  

• 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 = 0.01.

• We cannot conclude that the sample mean is greater than 73.

• We conclude that the sample mean is greater than 73.

• We cannot conclude that the population mean is greater than 73.

• We conclude that the population mean is greater than 73.

b-1. Calculate the p-value if the above sample mean was based on a sample of 118 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 = 0.01?
  

• 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 = 0.01.

• We conclude that the sample mean is greater than 73.

• We cannot conclude that the sample mean is greater than 73.

• We conclude that the population mean is greater than 73.

• We cannot conclude that the population mean is greater than 73.

Answer 1

a-1) Zstat = (xbar - mu)/(s/√n).

Therefore, Zstat becomes (74.3-73)/(3.7/√51) = 2.5 . Since it's an upper tail test, therefore p-value is given by (1- ¢(z)) = (1- ¢(2.5)) = 1-0.9938 = 0.0062.

a-2) At alpha = 0.01, we reject the null hypothesis since p<alpha. (Option A)

a-3) We conclude that the population mean is greater than 73 since we have rejected the null. (Option D)

b-1) For n = 118, Zstat becomes (74.3-73)/(3.7/√118) = 3.82 and thereby p-value becomes (1- ¢(3.82)) = (1- 1) = 0

b-2) We'll reject null hypothesis since again p-value is less than alpha (Option A)

b-3) We again conclude that the population mean is greater than 73 (Option C)