Question 1

A test statistic is computed from sample data in hypothesis testing and is used in making a decision about whether or not to reject the null hypothesis.

Accepted Answer

The test statistic is separate from alpha which we, as the researcher, set ourselves.

Question 2

The larger the p-value, the more we doubt the null hypothesis.

Accepted Answer

The larger the p-value, the greater the doubt the alternative hypothesis.

Question 3

When the null hypothesis is not rejected, there is no possibility of making a Type I error.

Accepted Answer

A Type I error centers around a true null hypothesis and therefore it cannot be false.

Question 4

We are testing H₀: μ ≤ 8; versus H_A: μ > 8. Given α = .01, n = 25, = 8.112, and s = .16, we should reject the H₀. Assume that the population from which the sample is selected is normally distributed.

Accepted Answer

H₀: μ ≤ 8 H_A: μ > 8 t == 3.5 t_.01,24= 2.492 3.5 > 2.492, reject H₀

Question 5

We are testing H₀: μ ≥ 22; versus H_A: μ < 22. Given α = .01, n = 100, = 21.431, and σ = 1.295, we should not reject H₀.

Accepted Answer

H₀: μ ≥ 22 H_A: μ < 22 Z === −4.394 Z_.01 = −2.33 −4.394 < −2.33, reject H₀

Question 6

When applying either the critical value rule or the p-value rule about a single mean, other relevant factors held constant, increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type II error.

Accepted Answer

When you increase alpha, you are more likely to reject the null hypothesis because you are allowing yourself more room for error.

Question 7

As the level of significance, α, increases, we are more likely to reject the null hypothesis.

Accepted Answer

This is because we are giving ourselves more room for error.

Question 8

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level for this test is .10, the null hypothesis would be rejected.

Accepted Answer

Since the calculated p-value is less than the significance level, you would reject the null hypothesis.

Question 9

A Type II error is failing to reject a false null hypothesis.

Accepted Answer

This means you had enough statistical evidence to reject the null hypothesis in favor of the alternative, but you did not.

Question 10

You cannot make a Type II error when the null hypothesis is true.

Accepted Answer

A Type II error centers around a false null hypothesis, so therefore it cannot be true.

Question 11

A Type I error is rejecting a true null hypothesis.

Accepted Answer

This means that you thought there was enough statistical evidence to reject the null hypothesis in favor of the alternative, but there is not.

Question 12

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .045 for the test. If the significance level (α) for this test is .05, the null hypothesis would be rejected.

Accepted Answer

Since the calculated p-value is less than the significance level, you would reject the null hypothesis.

Question 13

Using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.

Accepted Answer

If the level of significance (α) is less than the p-value, we fail to reject the null hypothesis.

Question 14

Alpha (α) is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.

Accepted Answer

α is the probability of a Type I error, which means rejecting the null hypothesis when it should be retained.

Question 15

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

Accepted Answer

You cannot accept the null hypothesis; you can only find evidence against it.

Question 16

The level of significance, α, indicates the probability of rejecting a false null hypothesis.

Accepted Answer

The level of significance is the probability of rejecting a true null hypothesis.

Question 17

Everything else being constant, increasing the sample size decreases the probability of committing a Type II error.

Accepted Answer

If you have a larger sample size, you are more likely to reject the null hypothesis when it is untrue.

Question 18

When the null hypothesis is true, there is no possibility of making a Type I error.

Accepted Answer

There is a possibility of making a Type I error when the null hypothesis is true.

Question 19

When applying either the critical value rule or the p-value rule about a single mean, reducing the level of significance (α) will increase the size of the rejection region.

Accepted Answer

Reducing the level of significance will decrease the rejection area.

Question 20

When applying either the critical value rule or the p-value rule about a single mean, other relevant factors held constant, increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type I error.

Accepted Answer

Increasing α will increase the probability of a Type I error.

Quiz 10: Hypothesis Testing