Question 1

If a null hypothesis was not rejected at the 0.10 level of significance,it will be rejected at a 0.05 level of significance based on the same sample results.

Accepted Answer

This statement is false. If the null hypothesis was not rejected at the 0.10 level of significance, it may or may not be rejected at the 0.05 level of significance based on the same sample results. The decision to reject the null hypothesis depends on the severity of the test and the strength of the evidence against the null hypothesis.

Question 2

Generally speaking,the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Accepted Answer

The alternative hypothesis is the statement that the researcher wants to prove, while the null hypothesis is the opposite or alternative statement that the researcher wants to reject. Therefore, business researchers generally state their hypotheses in the alternative hypothesis.

Question 3

Whenever hypotheses are established such that the alternative hypothesis is "μ ≠ 8",where μ is the population mean,the hypothesis test would be a two-tailed test.

Accepted Answer

A two-tailed test is used when the alternative hypothesis is that the population mean is not equal to a certain value or range of values. In this case, the alternative hypothesis is that μ is not equal to 8, which could mean it is either greater than or less than 8, making it a two-tailed test.

Question 4

In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown.In this case the researcher cannot use the z test.

Accepted Answer

When the population standard deviation is unknown, the researcher must use a t-test instead of a z-test.

Question 5

If a null hypothesis was rejected at the 0.025 level of significance,it will be rejected at a 0.01 level of significance based on the same sample results.

Accepted Answer

If a null hypothesis is rejected at a lower level of significance (e.g. 0.025), it will also be rejected at a higher level of significance (e.g. 0.01), since the higher level of significance is more stringent and requires stronger evidence to reject the null hypothesis.

Question 6

The probability of committing a Type I error is called the power of the test.

Accepted Answer

The probability of committing a Type I error is actually the significance level of the test. The power of the test is the probability of correctly rejecting a false null hypothesis (i.e. avoiding a Type II error).

Question 7

When a false null hypothesis is rejected,the researcher has made a Type II error.

Accepted Answer

When a false null hypothesis is rejected, it means that the researcher has made a correct decision, not an error. A Type II error occurs when a true null hypothesis is not rejected.

Question 8

If a null hypothesis is not rejected at the 0.05 level of significance,the p-value is bigger than 0.05

Accepted Answer

If the null hypothesis is not rejected at the 0.05 level of significance, it means that the p-value is greater than 0.05. The p-value represents the probability of obtaining the observed results or more extreme results if the null hypothesis is true. If the p-value is greater than the level of significance (in this case 0.05), then we fail to reject the null hypothesis.

Question 9

The probability of type II error becomes bigger if the level of significance is changed from 0.01 to 0.05.

Accepted Answer

The answer of The probability of type II error becomes...

Question 10

When a true null hypothesis is rejected,the researcher has made a Type I error.

Accepted Answer

This statement is true. A Type I error occurs when a researcher rejects a true null hypothesis, meaning that they incorrectly conclude that there is a significant difference or relationship when none actually exists.

Question 11

The rejection and nonrejection regions are divided by a point called the critical value.

Accepted Answer

This is true. The critical value is the boundary point that determines whether a test statistic falls in the rejection or nonrejection region, and thus determines whether the null hypothesis is rejected or not.

Question 12

Whenever hypotheses are established such that the alternative hypothesis is "μ>8",where μ is the population mean,the hypothesis test would be a two-tailed test.

Accepted Answer

If the alternative hypothesis is "μ>8", it means we are only interested in rejecting the null hypothesis if the sample mean is significantly greater than 8. Therefore, it would be a one-tailed test, not a two-tailed test.

Question 13

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

Accepted Answer

The rejection region becomes larger if the level of significance is increased from 0.01 to 0.05, as the threshold for rejecting the null hypothesis becomes less strict.

Question 14

Hypotheses are tentative explanations of a principle operating in nature.

Accepted Answer

Hypotheses are proposed explanations or predictions based on limited evidence and subject to further testing and verification. They are tentative and can be modified or discarded based on new data or observations.

Question 15

The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.

Accepted Answer

The null and alternative hypotheses must be mutually exclusive, meaning that they cannot both be true at the same time. They must also be collectively exhaustive, meaning that they must account for all possible outcomes or explanations. Therefore, both conditions need to be satisfied for the hypotheses to be valid.

Question 16

In testing hypotheses,the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

Accepted Answer

In testing hypotheses, the researcher initially assumes that the null hypothesis is true and uses the sample data to either reject it in favor of the alternative hypothesis or fail to reject it.

Question 17

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

Accepted Answer

The first step is to establish a null hypothesis (H0) that assumes no effect or no difference, and an alternative hypothesis (H1) that proposes an effect, difference, or relationship. The null is not assumed to be true or false initially; it's a starting point for testing.

Question 18

Power is equal to (1 -$\beta$),the probability of a test rejecting the null hypothesis that is indeed false.

Accepted Answer

The statement is true, as power is defined as the probability of correctly rejecting the null hypothesis when it is indeed false. The formula provided calculates the power based on the effect size (S1), significance level (α), and sample size (n).

Question 19

Whenever hypotheses are established such that the alternative hypothesis is "μ > 8",where μ is the population mean,the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.

Accepted Answer

This statement is true. The p-value represents the probability of obtaining a sample mean equal to or more extreme than the observed sample mean assuming the null hypothesis (μ = 8) is true. In this case, since the alternative hypothesis is μ > 8, we are specifically interested in the probability of observing a sample mean greater than the observed sample mean.

Question 20

When a researcher fails to reject a false null hypothesis,a Type II error has been committed.

Accepted Answer

A Type II error occurs when the null hypothesis is false, but the researcher fails to reject it, mistakenly concluding there is not enough evidence to support the alternative hypothesis.

Quiz 9: Statistical Inference: Hypothesis Testing for Single Populations

If a null hypothesis was not rejected at the 0.10 level of significance,it will be rejected at a 0.05 level of significance based on the same sample results.

Generally speaking,the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Whenever hypotheses are established such that the alternative hypothesis is "μ ≠ 8",where μ is the population mean,the hypothesis test would be a two-tailed test.

In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown.In this case the researcher cannot use the z test.

If a null hypothesis was rejected at the 0.025 level of significance,it will be rejected at a 0.01 level of significance based on the same sample results.

The probability of committing a Type I error is called the power of the test.

When a false null hypothesis is rejected,the researcher has made a Type II error.

If a null hypothesis is not rejected at the 0.05 level of significance,the p-value is bigger than 0.05

The probability of type II error becomes bigger if the level of significance is changed from 0.01 to 0.05.

When a true null hypothesis is rejected,the researcher has made a Type I error.

The rejection and nonrejection regions are divided by a point called the critical value.

Whenever hypotheses are established such that the alternative hypothesis is "μ>8",where μ is the population mean,the hypothesis test would be a two-tailed test.

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

Hypotheses are tentative explanations of a principle operating in nature.

The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.

In testing hypotheses,the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

Power is equal to (1 - $\beta$ ),the probability of a test rejecting the null hypothesis that is indeed false.

Whenever hypotheses are established such that the alternative hypothesis is "μ > 8",where μ is the population mean,the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.

When a researcher fails to reject a false null hypothesis,a Type II error has been committed.

Quiz 9: Statistical Inference: Hypothesis Testing for Single Populations

If a null hypothesis was not rejected at the 0.10 level of significance,it will be rejected at a 0.05 level of significance based on the same sample results.

Generally speaking,the hypotheses that business researchers want to prove are stated in the alternative hypothesis.

Whenever hypotheses are established such that the alternative hypothesis is "μ ≠ 8",where μ is the population mean,the hypothesis test would be a two-tailed test.

In many cases a business researcher gathers data to test a hypothesis about a single population mean and the value of the population standard deviation is unknown.In this case the researcher cannot use the z test.

If a null hypothesis was rejected at the 0.025 level of significance,it will be rejected at a 0.01 level of significance based on the same sample results.

The probability of committing a Type I error is called the power of the test.

When a false null hypothesis is rejected,the researcher has made a Type II error.

If a null hypothesis is not rejected at the 0.05 level of significance,the p-value is bigger than 0.05

The probability of type II error becomes bigger if the level of significance is changed from 0.01 to 0.05.

When a true null hypothesis is rejected,the researcher has made a Type I error.

The rejection and nonrejection regions are divided by a point called the critical value.

Whenever hypotheses are established such that the alternative hypothesis is "μ>8",where μ is the population mean,the hypothesis test would be a two-tailed test.

The rejection region for a hypothesis test becomes smaller if the level of significance is changed from 0.01 to 0.05.

Hypotheses are tentative explanations of a principle operating in nature.

The null and the alternative hypotheses must be mutually exclusive and collectively exhaustive.

In testing hypotheses,the researcher initially assumes that the alternative hypothesis is true and uses the sample data to reject it.

The first step in testing a hypothesis is to establish a true null hypothesis and a false alternative hypothesis.

Power is equal to (1 - β\betaβ ),the probability of a test rejecting the null hypothesis that is indeed false.

Whenever hypotheses are established such that the alternative hypothesis is "μ > 8",where μ is the population mean,the p-value is the probability of observing a sample mean greater than the observed sample mean assuming that μ = 8.

When a researcher fails to reject a false null hypothesis,a Type II error has been committed.

Power is equal to (1 - $\beta$ ),the probability of a test rejecting the null hypothesis that is indeed false.