Question

In order to conduct a hypothesis test for the population proportion, you sample 485 observations that result in 262 successes. (You may find it useful to reference the appropriate table: z table or t table) H0: p ≥ 0.57; HA: p < 0.57. 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. 0.01 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-3. At the 0.10 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. a-4. Interpret the results at α = 0.10 We conclude that the population mean is less than 0.57. We cannot conclude that the population mean is less than 0.57. We conclude that the population proportion is less than 0.57. We cannot conclude that the population proportion is less than 0.57. H0: p = 0.57; HA: p ≠ 0.57. 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 0.10 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 α = 0.10. We conclude that the population mean differs from 0.57. We cannot conclude that the population mean differs from 0.57. We conclude the population proportion differs from 0.57. We cannot conclude that the population proportion differs from 0.57.

Answer 1

Part A.

Given a sample of N = 485 observations that result in X =262 successes. Thus the sample proportion is computed as:

Given the Hypotheses are:

H₀: p ≥ 0.57;

H_A: p < 0.57

Now based on the hypothesis it will be a left-tailed test.

Rejection region:

Based on the given significance level as 0.10 reject the Ho if P-value is less than 0.10.

a1) Test statistic:

Z = -1.33

a2) P-value:

The P-value is computed using the excel formula for normal distribution which is calculated using the excel formula for normal distribution which is =NORM.S.DIST(-1.325, TRUE) , thus the P-value is computed as 0.0925.

Thus 0.05 < p-value < 0.10.

a3) Conclusion:

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

a4) Interpretation:

We conclude that the population proportion is less than 0.57.

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Part B

For the hypotheses:

H0: p = 0.57;

HA: p ≠ 0.57

Based on the hypothesis it will be a two-tailed test.

Rejection region:

Based on the given significance level as 0.10 reject the Ho if P-value is less than 0.10.

b1) Test statistic:

Z = -1.33

b2) P-value:

The P-value is computed using the excel formula for normal distribution which is calculated using the excel formula for normal distribution which is =2* NORM.S.DIST(-1.325, TRUE) , thus the P-value is computed as 0.1852.

Thus p-value > 0.10.

b3) . Conclusion:

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

b4). Interpreataion:

We cannot conclude that the population proportion differs from 0.57.

Note: Feel free to ask if query remains.