Question 1

Which of the following is NOT a common step in hypothesis testing: A)determine the null and alternative hypotheses B)specify the level of significance $\alpha$ C)collect the sample data and compute the value of the test statistic D)use $\alpha$ to determine the critical value and the rejection rule E)compute the p-value based on the test statistic and compare it to $\beta$ to determine whether to reject H₀

Accepted Answer

In hypothesis testing, the p-value is compared to the level of significance $\alpha$, not $\beta$, to determine whether to reject the null hypothesis $H_0$.

Question 2

In hypothesis testing, the critical value is a number that establishes the boundary of the reject H₀ region of the test.

Accepted Answer

The critical value is used to determine the threshold at which the null hypothesis (H0) is rejected in favor of the alternative hypothesis.

Question 3

When the p-value is used for hypothesis testing, the null hypothesis is rejected when the p-value < $\alpha$.

Accepted Answer

The null hypothesis is rejected when the p-value is less than the significance level ($\alpha$), indicating that the observed data is unlikely under the null hypothesis.

Question 4

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 2.5% could be used.

Accepted Answer

A 95% confidence interval corresponds to a two-tailed hypothesis test with a significance level of 5%, not 2.5%. A 2.5% significance level would correspond to a 97.5% confidence interval.

Question 5

A student believes that the average grade on the final examination in statistics is greater than 85.To make her case, she will take a sample of scores and test a skeptical null hypothesis.The correct set of hypotheses is A)H₀: $\mu$ < 85; H_a: $\mu$ ≥ 85 B)H₀: $\mu$ > 85; H_a: $\mu$≤ 85 C)H₀: $\mu$≤ 85; H_a: $\mu$ > 85 D)H₀: $\mu$ = 85; H_a: $\mu$$\neq$85 E)none of the above

Accepted Answer

The correct set of hypotheses for testing if the average grade is greater than 85 involves setting the null hypothesis (H0) as the average being less than or equal to 85 (μ ≤ 85), and the alternative hypothesis (Ha) as the average being greater than 85 (μ > 85). This is because the null hypothesis typically represents the status quo or a statement of no effect, which the alternative hypothesis seeks to disprove.

Question 6

In hypothesis testing, we reject the null hypothesis if the p-value > $\alpha$.

Accepted Answer

We reject the null hypothesis if the p-value is less than or equal to the significance level (alpha), typically represented as p-value ≤ α. The value F1F1F1S1αF1F1F10 is not a commonly used threshold for rejecting the null hypothesis.

Question 7

The p-value measures the probability that, if the null hypothesis is true, we would randomly produce a sample result at least as unlikely as the sample result that we actually produced.

Accepted Answer

The p-value is a measure used in statistical hypothesis testing to quantify the evidence against the null hypothesis. It represents the probability of observing a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

Question 8

In hypothesis testing, we reject the null hypothesis if the p-value < $\alpha$.

Accepted Answer

The statement is essentially correct, although it seems to contain formatting or typographical errors. In hypothesis testing, we reject the null hypothesis if the p-value is less than the significance level (often denoted as alpha, α), which is what the statement is attempting to convey despite the garbled symbols.

Question 9

In the standard forms for the null and alternative hypotheses, the equality part of a hypothesis can appear in either hypothesis.

Accepted Answer

In the standard forms for the null (H0) and alternative hypotheses (H1 or Ha), the equality part (such as =, ≤, or ≥) appears in the null hypothesis, while the alternative hypothesis contains the inequality part (such as ≠, >, or <).

Question 10

The level of significance in hypothesis testing is the probability of accepting a true null hypothesis.

Accepted Answer

The level of significance in hypothesis testing is the probability of rejecting a true null hypothesis, also known as the Type I error rate.

Question 11

The magnitude of z for a two-tailed hypothesis test of a population mean is greater than it would be in a one-tail hypothesis test given the same level of significance.

Accepted Answer

In a two-tailed hypothesis test, the critical region is split between the two tails of the distribution, requiring a larger z-value to reach the same level of significance as compared to a one-tailed test, where the entire critical region is in one tail.

Question 12

The probability of making a Type I error is typically denoted by $\beta$.

Accepted Answer

The probability of making a Type I error is typically denoted by the symbol $\alpha$, not the symbols provided in the question.

Question 13

Which of the following does not need to be known in order to compute the p-value?
A)knowledge of whether the test is one-tailed or two-tailed
B)the value of the test statistic
C)the level of significance
D)a, b, and c are all unnecessary
E)a, b and c are all needed

Accepted Answer

The p-value can be computed without knowing the level of significance, as it is a measure of the evidence against the null hypothesis provided by the sample data. The level of significance is used after computing the p-value to make a decision regarding the null hypothesis.

Question 14

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 5% could be used.

Accepted Answer

Both a 95% confidence interval and a two-tailed hypothesis test with a significance level of 5% are methods to determine if there is enough evidence to reject a null hypothesis about a population mean. If the confidence interval does not include the hypothesized mean, or if the p-value in the hypothesis test is less than 0.05, the null hypothesis would be rejected.

Question 15

Which of the following best describe(s) the significance level? A)it is the probability of rejecting a true null hypothesis B)it is denoted by $\alpha$ C)it is the probability of making a Type I error D)it is used to define the boundary of the reject H₀ region E)all of the above

Accepted Answer

The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is actually true, which is the definition of a Type I error. It is used to define the critical boundary beyond which we reject the null hypothesis. Therefore, all the statements A, C, and D correctly describe aspects of the significance level, making E the correct choice.

Question 16

The level of significance, $\alpha$ is the probability of making a Type II error, which is rejecting a true null hypothesis.

Accepted Answer

The level of significance is the probability of making a Type I error, which is rejecting a true null hypothesis. A Type II error is failing to reject a false null hypothesis.

Question 17

Type I error occurs when a false null hypothesis is rejected.

Accepted Answer

Type I error occurs when a true null hypothesis is incorrectly rejected.

Question 18

The p-value is the probability associated with the test statistic while alpha $\alpha$ is the probability associated with the critical value.

Accepted Answer

The p-value is indeed the probability of obtaining a test statistic at least as extreme as the one observed, given that the null hypothesis is true. Alpha (α) is the predetermined significance level, representing the probability threshold below which the null hypothesis is rejected, often associated with the critical value that separates the rejection region from the non-rejection region in hypothesis testing.

Question 19

The level of significance in hypothesis testing, $\alpha$, measures the maximum probability of making a Type II error, which is the probability of accepting a false null hypothesis.

Accepted Answer

The level of significance measures the maximum probability of making a Type I error, which is the probability of rejecting a true null hypothesis.

Question 20

The value of the test statistic for a two-tail hypothesis test for a population mean is the same as for a one-tail hypothesis test.

Accepted Answer

The value of the test statistic itself does not change between one-tail and two-tail tests; what changes is how the test statistic is evaluated against the critical value(s) to determine significance.

Quiz 9: Statistical Hypothesis Testing: Hypothesis Tests for a Population Mean

Which of the following is NOT a common step in hypothesis testing:

In hypothesis testing, the critical value is a number that establishes the boundary of the reject H₀ region of the test.

When the p-value is used for hypothesis testing, the null hypothesis is rejected when the p-value < $\alpha$ .

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 2.5% could be used.

A student believes that the average grade on the final examination in statistics is greater than 85.To make her case, she will take a sample of scores and test a skeptical null hypothesis.The correct set of hypotheses is

In hypothesis testing, we reject the null hypothesis if the p-value > $\alpha$ .

The p-value measures the probability that, if the null hypothesis is true, we would randomly produce a sample result at least as unlikely as the sample result that we actually produced.

In hypothesis testing, we reject the null hypothesis if the p-value < $\alpha$ .

In the standard forms for the null and alternative hypotheses, the equality part of a hypothesis can appear in either hypothesis.

The level of significance in hypothesis testing is the probability of accepting a true null hypothesis.

The magnitude of z for a two-tailed hypothesis test of a population mean is greater than it would be in a one-tail hypothesis test given the same level of significance.

The probability of making a Type I error is typically denoted by $\beta$ .

Which of the following does not need to be known in order to compute the p-value?

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 5% could be used.

Which of the following best describe(s) the significance level?

The level of significance, $\alpha$ is the probability of making a Type II error, which is rejecting a true null hypothesis.

Type I error occurs when a false null hypothesis is rejected.

The p-value is the probability associated with the test statistic while alpha $\alpha$ is the probability associated with the critical value.

The level of significance in hypothesis testing, $\alpha$ , measures the maximum probability of making a Type II error, which is the probability of accepting a false null hypothesis.

The value of the test statistic for a two-tail hypothesis test for a population mean is the same as for a one-tail hypothesis test.

Quiz 9: Statistical Hypothesis Testing: Hypothesis Tests for a Population Mean

Which of the following is NOT a common step in hypothesis testing:

In hypothesis testing, the critical value is a number that establishes the boundary of the reject H0 region of the test.

When the p-value is used for hypothesis testing, the null hypothesis is rejected when the p-value < α\alphaα .

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 2.5% could be used.

A student believes that the average grade on the final examination in statistics is greater than 85.To make her case, she will take a sample of scores and test a skeptical null hypothesis.The correct set of hypotheses is

In hypothesis testing, we reject the null hypothesis if the p-value > α\alphaα .

The p-value measures the probability that, if the null hypothesis is true, we would randomly produce a sample result at least as unlikely as the sample result that we actually produced.

In hypothesis testing, we reject the null hypothesis if the p-value < α\alphaα .

In the standard forms for the null and alternative hypotheses, the equality part of a hypothesis can appear in either hypothesis.

The level of significance in hypothesis testing is the probability of accepting a true null hypothesis.

The magnitude of z for a two-tailed hypothesis test of a population mean is greater than it would be in a one-tail hypothesis test given the same level of significance.

The probability of making a Type I error is typically denoted by β\betaβ .

Which of the following does not need to be known in order to compute the p-value?

To decide whether to reject a null hypothesis about a population mean, a 95% confidence interval or two-tailed hypothesis test with a significance level of 5% could be used.

Which of the following best describe(s) the significance level?

The level of significance, α\alphaα is the probability of making a Type II error, which is rejecting a true null hypothesis.

Type I error occurs when a false null hypothesis is rejected.

The p-value is the probability associated with the test statistic while alpha α\alphaα is the probability associated with the critical value.

The level of significance in hypothesis testing, α\alphaα , measures the maximum probability of making a Type II error, which is the probability of accepting a false null hypothesis.

The value of the test statistic for a two-tail hypothesis test for a population mean is the same as for a one-tail hypothesis test.

In hypothesis testing, the critical value is a number that establishes the boundary of the reject H₀ region of the test.

When the p-value is used for hypothesis testing, the null hypothesis is rejected when the p-value < $\alpha$ .

In hypothesis testing, we reject the null hypothesis if the p-value > $\alpha$ .

In hypothesis testing, we reject the null hypothesis if the p-value < $\alpha$ .

The probability of making a Type I error is typically denoted by $\beta$ .

The level of significance, $\alpha$ is the probability of making a Type II error, which is rejecting a true null hypothesis.

The p-value is the probability associated with the test statistic while alpha $\alpha$ is the probability associated with the critical value.

The level of significance in hypothesis testing, $\alpha$ , measures the maximum probability of making a Type II error, which is the probability of accepting a false null hypothesis.