Question

In order to conduct a hypothesis test for the population proportion, you sample 400 observations that result in 212 successes. (You may find it useful to reference the appropriate table: z table or t table)

H₀: p ≥ 0.54; H_A: p < 0.54.

a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

a-2. Find the p-value.

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

• p-value < 0.01

• 0.01 p-value < 0.025

a-3. At the 0.01 significance level, What is the conclusion?

• Do not reject H₀ since the p-value is smaller than significance level.

• Do not reject H₀ since the p-value is greater than significance level.

• Reject H₀ since the p-value is smaller than significance level.

• Reject H₀ since the p-value is greater than significance level.

a-4. Interpret the results at αα = 0.01

• We cannot conclude that the population mean is less than 0.54.

• We conclude that the population mean is less than 0.54.

• We cannot conclude that the population proportion is less than 0.54.

• We conclude that the population proportion is less than 0.54.

H₀: p = 0.54; H_A: p ≠ 0.54.

b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

b-2. 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

b-3. At the 0.01 significance level, What is the conclusion?

• Reject H₀ since the p-value is greater than significance level.

• Reject H₀ since the p-value is smaller than significance level.

• Do not reject H₀ since the p-value is greater than significance level.

• Do not reject H₀ since the p-value is smaller than significance level.

b-4. Interpret the results at αα = 0.01.

• We conclude that the population mean differs from 0.54.

• We cannot conclude that the population mean differs from 0.54.

• We conclude the population proportion differs from 0.54.

• We cannot conclude that the population proportion differs from 0.54.

Answer 1