AP Statistics Exam 2018: Investigative Task

When does a Type II error occur?

• A Type II error occurs when the null hypothesis is true, but it is rejected.

• A Type II error occurs when the null hypothesis is true, but it is not rejected.

• A Type II error occurs when the alternative hypothesis is true, but the null hypothesis is rejected.

• A Type II error occurs when the alternative hypothesis is true, but the null hypothesis is not rejected.

Describe a Type II error in the context of the hypothesis test.

• A Type II error occurs when the actual mean systolic blood pressure of employees is 122 mmHg, but the null hypothesis that it is 122 mmHg is rejected.

• A Type II error occurs when the actual mean systolic blood pressure of employees is 122 mmHg, but the null hypothesis that it is 122 mmHg is not rejected.

• A Type II error occurs when the actual mean systolic blood pressure of employees is greater than 122 mmHg, but the null hypothesis that it is 122 mmHg is rejected.

• A Type II error occurs when the actual mean systolic blood pressure of employees is greater than 122 mmHg, but the null hypothesis that it is 122 mmHg is not rejected.

Assume that σ, the standard deviation of the systolic blood pressure of all employees at the corporation, is 15 mmHg. If μ = 122, the sampling distribution of x̄ for samples of size 100 is approximately normal with a mean of 122 mmHg and a standard deviation of 1.5 mmHg.

What values of z would represent sufficient evidence to reject the null hypothesis at the significance level of α = 0.05?

• z < -1.96

• z < -1.645

• z > 1.645

• z > 1.96

Tags

CCSS.HSS.ID.A.4

Assume that σ, the standard deviation of the systolic blood pressure of all employees at the corporation, is 15 mmHg. If μ = 122, the sampling distribution of x̄ for samples of size 100 is approximately normal with a mean of 122 mmHg and a standard deviation of 1.5 mmHg.

The null hypothesis will be rejected when z > 1.645.

What values of the sample mean x̄ would represent sufficient evidence to reject the null hypothesis at the significance level of α = 0.05?

• x̄ > 1.645

• x̄ = 124.468

• x̄ > 124.468

• x̄ = 146.675

• x̄ > 146.675

Tags

CCSS.HSS.ID.A.4

The actual mean systolic blood pressure of all employees at the corporation is 125 mmHg, not the hypothesized value of 122 mmHg, and the standard deviation is 15 mmHg.

What are the mean and standard deviation of the sampling distribution of the sample mean when the true mean is 125 mmHg?

• μ_x̄ = 122, σ_x̄ = 1.5

• μ_x̄ = 122, σ_x̄ = 15

• μ_x̄ = 124.468, σ_x̄ = 1.5

• μ_x̄ = 125, σ_x̄ = 1.5

• μ_x̄ = 125, σ_x̄ = 15

The actual mean systolic blood pressure of all employees at the corporation is 125 mmHg, not the hypothesized value of 122 mmHg, and the standard deviation is 15 mmHg.

The sampling distribution of the sample mean when the true mean is 125 mmHg has the following characteristics: μ_x̄ = 125, σ_x̄ = 1.5.

Using the actual mean of 125 mmHg and the fact that the null hypothesis will be rejected for x̄ > 124.468, determine the probability that the null hypothesis will be rejected.

• .0500

• .3714

• .4859

• .5141

• .6386

The actual mean systolic blood pressure of all employees at the corporation is 125 mmHg, not the hypothesized value of 122 mmHg, and the standard deviation is 15 mmHg.

The probability that the null hypothesis will be rejected is .6386. What is the statistical term for this probability?

• The power of the test

• The beta level

• The p-value

• The alpha level

• The significance level

The actual mean systolic blood pressure of all employees at the corporation is 125 mmHg, not the hypothesized value of 122 mmHg, and the standard deviation is 15 mmHg.

Suppose the size of the sample of employees to be selected is greater than 100. Would the probability of rejecting the null hypothesis be greater than, less than, or equal to the probability of rejecting the null hypothesis with a sample size of 100?

• Greater

• Less

• Equal

The actual mean systolic blood pressure of all employees at the corporation is 125 mmHg, not the hypothesized value of 122 mmHg, and the standard deviation is 15 mmHg.

Suppose the size of the sample of employees to be selected is greater than 100. The probability of rejecting the null hypothesis is greater than the probability of rejecting the null hypothesis with a sample size of 100. Why is this?

• The standard deviation of the sampling distribution decreases, and the minimum value of x̄ for which the null hypothesis will be rejected decreases.

• The standard deviation of the sampling distribution stays the same, but the minimum value of x̄ for which the null hypothesis will be rejected decreases.

• The standard deviation of the sampling distribution increases, and the minimum value of x̄ for which the null hypothesis will be rejected decreases.

• The standard deviation of the sampling distribution decreases, and the minimum value of x̄ for which the null hypothesis will be rejected increases.

• The standard deviation of the sampling distribution increases, and the minimum value of x̄ for which the null hypothesis will be rejected increases.