Question

Exercise 9-59 Algo

In order to conduct a hypothesis test for the population proportion, you sample 500 observations that result in 200 successes. (You may find it useful to reference the appropriate table: z table or t table)

H₀: p ≥ 0.41; H_A: p < 0.41.

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 0.05 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 = 0.05

• We cannot conclude that the population mean is less than 0.41.

• We conclude that the population mean is less than 0.41.

• We cannot conclude that the population proportion is less than 0.41.

• We conclude that the population proportion is less than 0.41.

H₀: p = 0.41; H_A: p ≠ 0.41.

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 0.05 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 = 0.05.

• We conclude that the population mean differs from 0.41.

• We cannot conclude that the population mean differs from 0.41.

• We conclude the population proportion differs from 0.41.

• We cannot conclude that the population proportion differs from 0.41.

Answer 1

a1)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4 - 0.41)/sqrt(0.41*(1-0.41)/500)
z = -0.45

a2)

P-value Approach
P-value = 0.3264
p-value > 0.10

a3)

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

a4)

We cannot conclude that the population mean is less than 0.41.

b1)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.4 - 0.41)/sqrt(0.41*(1-0.41)/500)
z = -0.45

b2)

P-value = 0.6527
As P-value >= 0.05, fail to reject null hypothesis.

p-value > 0.10

b3)

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

a4)

We cannot conclude that the population mean differs from 0.41.