Question 1

The researcher's null hypothesis is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The critical values of chi-square for a two-tailed test at α = .05 are: A)8.672 and 27.59 B)7.564 and 30.19 C)-1.960 and +1.960 D)9.390 and 28.87

Accepted Answer

The critical values of chi-square for a two-tailed test depend on the degrees of freedom (n-1) and the significance level (α). For n = 18, degrees of freedom = 17. At α = .05 for a two-tailed test, the critical values for 17 degrees of freedom are 7.564 and 30.19, which correspond to the lower and upper critical values, respectively. Choices A, C, and D do not match the correct critical values for a chi-square distribution with 17 degrees of freedom at the .05 significance level.

Question 2

In a statistical test we:
A)try to reject the null hypothesis.
B)try to prove the alternative hypothesis.
C)choose a null hypothesis that is easy to reject.
D)choose a large level of significance if possible.

Accepted Answer

In a statistical test, the null hypothesis is assumed to be true until proven otherwise. Therefore, the aim is to gather evidence that suggests that the null hypothesis should be rejected in favor of the alternative hypothesis. This means that the correct choice is to try to reject the null hypothesis (choice A). The other options are not correct: we are not trying to prove the alternative hypothesis (choice B), we do not choose a null hypothesis that is easy to reject (choice C), and we do not aim for a large level of significance if possible (choice D).

Question 3

The researcher's null hypotheses is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The test statistic is: A)31.09. B)26.42. C)must know if it is a one-tailed test. D)must know α to answer.

Accepted Answer

The test statistic for testing a variance with known population mean is given by:

χ² = (n-1)s² / σ²

Substituting the given values, we get:

χ² = (25-1)(28.5) / 22 = 31.09

Therefore, the correct choice is A.

Question 4

The critical value in a hypothesis test:
A)is derived from the sample.
B)is determined by α and the type of test.
C)is another name for the null hypothesis.
D)is a dissenting view by scientific critics.

Accepted Answer

The critical value is determined by the level of significance (α) selected for the hypothesis test and the type of test being conducted. It is not derived from the sample, a term often used to describe the values obtained from the actual data collected. It is also not the same as the null hypothesis, which is a statement being tested in the hypothesis test. Finally, it is not a dissenting view by scientific critics, but rather a standard value used in statistical hypothesis testing.

Question 5

The decision rule is:
A)based on the sampling distribution and chosen level of significance.
B)specified so as to support the researcher's alternative hypothesis.
C)chosen after selecting the sample and calculating the test statistic.
D)specified by a panel of expert statisticians elected annually.

Accepted Answer

The decision rule is based on the sampling distribution and the chosen level of significance. It is determined before the sample is selected and the test statistic is calculated.

Question 6

The researcher's null hypotheses is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The test statistic is: A)34.09 B)20.72 C)14.77 D)must know α to answer.

Accepted Answer

The answer of The researcher's null hypotheses is H₀: σ²...

Question 7

If n = 25 and α = .05 in a right-tailed test of a mean with unknown σ, the critical value is: A)1.960 B)1.645 C)1.711 D).0179 Using d.f. = 24, t_.05 = 1.711 from AppendixD.

Accepted Answer

Since it is a right-tailed test, we need to find the critical value with a significance level of .05 and degrees of freedom of 24 (n-1). Using Appendix D, we find that the critical value for this scenario is 1.711. Therefore, the correct choice is C.

Question 8

In hypothesis testing, the value of β is: A)equal to 1 minus the probability of committing a Type I error. B)the probability of concluding H₀ when H₀ is true. C)the probability of concluding H₀ when H₁ is true.

Accepted Answer

Beta (β) is the probability of making a Type II error, which occurs when the null hypothesis is falsely accepted, meaning the test fails to detect an effect or difference that actually exists. Option C correctly describes this scenario, where the null hypothesis is incorrectly accepted as true when in fact the alternative hypothesis is true.

Question 9

In testing the hypotheses H₀: π ≤ π₀, H₁: π > π₀, we would use a: A)two-tailed test. B)left-tailed test. C)right-tailed test. D)breathalyzer test.

Accepted Answer

The hypothesis H₁: π > π₀ suggests that we are interested in determining if the true population proportion (π) is greater than a certain value (π₀), therefore, a right-tailed test is appropriate.

Question 10

A two-tailed hypothesis test:
A)would not be used if the test statistic could be negative.
B)will double the probability of rejecting the null hypothesis.
C)is used when the direction of the test is of no research interest.
D)would lead to rejection more often than a one-tailed test at the same α.

Accepted Answer

A two-tailed hypothesis test is used when the direction of the test is of no research interest, meaning the researcher is interested in determining whether the sample mean is different from some hypothesized value, but not in which direction. Therefore, it is not affected by the sign of the test statistic and will not double the probability of rejecting the null hypothesis. In fact, it would lead to rejection less often than a one-tailed test at the same α level since it has a smaller critical value.

Question 11

Regarding the probability of Type I error (α) and Type II error (β), which statement is true?
A)β > α
B)β < α
C)α + β = 1
D)Power = 1 - β.

Accepted Answer

Power of a test is defined as 1 - β, where β is the probability of making a Type II error.

Question 12

In hypothesis testing, Type I error is: A)always set at 5 percent. B)smaller than or equal to 5 percent. C)the probability of rejecting H₀ when H₀ is true. D)the probability of rejecting H₀ when H₁ is true.

Accepted Answer

Type I error is the probability of rejecting the null hypothesis (H₀) when it is actually true. It is not always set at 5 percent, but rather depends on the level of significance chosen by the researcher. It can be smaller or larger than 5 percent. Option D refers to a different scenario, where the null hypothesis is false.

Question 13

The rejection region in a hypothesis test:
A)is an area in the tail(s) of a sampling distribution.
B)is a consensus formed by trained statisticians.
C)is always set to correspond to α = .05 in the test.
D)is always equal to the p-value in the test.

Accepted Answer

The rejection region is an area in the tail(s) of a sampling distribution where we reject the null hypothesis if our test statistic falls there. It is determined by the level of significance (α) chosen for the test.

Question 14

We can assume that the sample proportion is normally distributed if:
A)we have 10 successes in the sample.
B)we have 10 failures in the sample.
C)we have both 10 successes and 10 failures in the sample.
D)the population is known.

Accepted Answer

In order for the sample proportion to be assumed to be normally distributed, the sample size has to be large enough, specifically having at least 10 successes and 10 failures. Choice A and B satisfy only one of the criteria, which is not sufficient. The population being known is not relevant to whether the sample proportion is normally distributed.

Question 15

The rejection region in a hypothesis test:
A)is an area in the tail(s) of a sampling distribution.
B)is a consensus formed by trained statisticians.
C)is always set to correspond to α = .05 in the test.
D)is always equal to the p-value in the test.

Accepted Answer

The rejection region is an area in the tail (or tails) of a sampling distribution that is used to determine whether to reject or fail to reject the null hypothesis in a hypothesis test. The exact location and size of the rejection region depends on the chosen significance level (often α = .05) and the type of test being conducted. The rejection region is not determined by a consensus of statisticians, is not always set to correspond to α = .05, and is not always equal to the p-value.

Question 16

The researcher's null hypothesis is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The critical value of chi-square for a right-tailed test at α = .05 is: A)1.960 B)1.645 C)13.85 D)36.42

Accepted Answer

To find the critical value of chi-square, we need to use the formula:

χ^2 = (n-1) * s^2 / σ^2

where n is the sample size, s^2 is the sample variance, and σ^2 is the hypothesized population variance.

Substituting the given values, we get:

χ^2 = (25-1) * 28.5 / 22 ≤ 31.4068

To find the critical value of chi-square for a right-tailed test at α = .05, we need to look up the value in the chi-square distribution table with (25-1) degrees of freedom and a probability of 0.95 (1-α). The closest value is 36.42, which corresponds to a probability of 0.95.

Therefore, the best choice is D, 36.42, because it is the critical value of chi-square for a right-tailed test at α = .05 with (25-1) degrees of freedom.

Question 17

For a right-tailed test of hypothesis for a population mean with known σ, the test statistic was z = 1.79. The p-value is:
A).0367
B).9633
C).1186
D).0179

Accepted Answer

The p-value for a right-tailed test with z = 1.79 is found by looking up the area to the right of 1.79 in the standard normal distribution, which is approximately 0.0367.

Question 18

The critical value in a hypothesis test:
A)is a test statistic calculated from the sample.
B)is a contradictory result from a different test.
C)is a cutoff between the rejection and nonrejection regions.
D)is another name for level of significance.

Accepted Answer

The critical value represents the cutoff point between the rejection and nonrejection regions in a hypothesis test. It is typically compared to the test statistic, which is calculated from the sample data, to determine whether the null hypothesis should be rejected. The level of significance, while related to the critical value, is not the same thing as it refers to the probability of rejecting the null hypothesis when it is actually true. Choice A is incorrect as it describes the test statistic, not the critical value. Choice B is incorrect as it does not relate to hypothesis testing.

Question 19

In the hypothesis H₀: μ = μ₀, the value of μ₀ is not derived from: A)the sample. B)past experience. C)a target or benchmark. D)a scientific theory.

Accepted Answer

The value of μ₀ in the hypothesis is not derived from the sample itself. It is typically predetermined based on past experience, a target or benchmark, or a scientific theory.

Question 20

The null hypothesis is:
A)often from a benchmark or historical value.
B)chosen after looking at the sample data.
C)what the researcher is trying to prove.
D)dependent on the level of significance.

Accepted Answer

The null hypothesis is typically a statement about a population parameter that represents the status quo, or the currently accepted value, which is often based on a benchmark or historical value.

Quiz 9: One-Sample Hypothesis Tests

The researcher's null hypothesis is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The critical values of chi-square for a two-tailed test at α = .05 are:

In a statistical test we:

The researcher's null hypotheses is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The test statistic is:

The critical value in a hypothesis test:

The decision rule is:

The researcher's null hypotheses is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The test statistic is:

If n = 25 and α = .05 in a right-tailed test of a mean with unknown σ, the critical value is:

In hypothesis testing, the value of β is:

In testing the hypotheses H₀: π ≤ π₀, H₁: π > π₀, we would use a:

A two-tailed hypothesis test:

Regarding the probability of Type I error (α) and Type II error (β) , which statement is true?

In hypothesis testing, Type I error is:

The rejection region in a hypothesis test:

We can assume that the sample proportion is normally distributed if:

The rejection region in a hypothesis test:

The researcher's null hypothesis is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The critical value of chi-square for a right-tailed test at α = .05 is:

For a right-tailed test of hypothesis for a population mean with known σ, the test statistic was z = 1.79. The p-value is:

The critical value in a hypothesis test:

In the hypothesis H₀: μ = μ₀, the value of μ₀ is not derived from:

The null hypothesis is:

Quiz 9: One-Sample Hypothesis Tests

The researcher's null hypothesis is H0: σ2 = 420. A sample of n = 18 items yields a sample variance of s2 = 512. The critical values of chi-square for a two-tailed test at α = .05 are:

In a statistical test we:

The researcher's null hypotheses is H0: σ2 ≤ 22. A sample of n = 25 items yields a sample variance of s2 = 28.5. The test statistic is:

The critical value in a hypothesis test:

The decision rule is:

The researcher's null hypotheses is H0: σ2 = 420. A sample of n = 18 items yields a sample variance of s2 = 512. The test statistic is:

If n = 25 and α = .05 in a right-tailed test of a mean with unknown σ, the critical value is:

In hypothesis testing, the value of β is:

In testing the hypotheses H0: π ≤ π0, H1: π > π0, we would use a:

A two-tailed hypothesis test:

Regarding the probability of Type I error (α) and Type II error (β) , which statement is true?

In hypothesis testing, Type I error is:

The rejection region in a hypothesis test:

We can assume that the sample proportion is normally distributed if:

The rejection region in a hypothesis test:

The researcher's null hypothesis is H0: σ2 ≤ 22. A sample of n = 25 items yields a sample variance of s2 = 28.5. The critical value of chi-square for a right-tailed test at α = .05 is:

For a right-tailed test of hypothesis for a population mean with known σ, the test statistic was z = 1.79. The p-value is:

The critical value in a hypothesis test:

In the hypothesis H0: μ = μ0, the value of μ0 is not derived from:

The null hypothesis is:

The researcher's null hypothesis is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The critical values of chi-square for a two-tailed test at α = .05 are:

The researcher's null hypotheses is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The test statistic is:

The researcher's null hypotheses is H₀: σ² = 420. A sample of n = 18 items yields a sample variance of s² = 512. The test statistic is:

In testing the hypotheses H₀: π ≤ π₀, H₁: π > π₀, we would use a:

The researcher's null hypothesis is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The critical value of chi-square for a right-tailed test at α = .05 is:

In the hypothesis H₀: μ = μ₀, the value of μ₀ is not derived from: