Question 1

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 1% level of
significance.

Accepted Answer

The null hypothesis will not be rejected because the sample mean of 257.3 W is not significantly higher than 250 W at the 1% level of significance, given the standard deviation and sample size.

Question 2

True or False: You should report only the results of hypothesis tests that show statistical
significance and omit those for which there is insufficient evidence in the findings.

Accepted Answer

Omitting non-significant results can lead to biased reporting and misinterpretation of the data, as it does not provide a complete picture of the research findings.

Question 3

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-Referring to Scenario 9-3, the appropriate hypotheses to determine if the manufacturer's claim
Appears reasonable are:

Accepted Answer

The answer of SCENARIO 9-3
An appliance manufacturer claims to have...

Question 4

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what would be a Type I error?

Accepted Answer

A Type I error occurs when the null hypothesis is rejected when it is actually true. In this scenario, the null hypothesis is that the person is a business major, so a Type I error would occur if the student incorrectly identifies the person as an agriculture major when they are actually a business major.

Question 5

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-True or False: Referring to Scenario 9-3, for this test to be valid, it is necessary that the power
consumption for microwave ovens has a normal distribution.

Accepted Answer

The validity of the test relies on the assumption that the sample mean follows a normal distribution, which is ensured if the population distribution is normal or the sample size is large enough (Central Limit Theorem).

Question 6

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the "actual level of significance" of the test?

Accepted Answer

The actual level of significance is the probability of rejecting the null hypothesis when it is actually true. In this case, it is the probability that the student incorrectly identifies a business major as an agriculture major. This is given as 16%, or 0.16. Therefore, the actual level of significance is 0.16, which corresponds to choice letter A.

Question 7

True or False: "What conclusions and interpretations can you reach from the results of the
hypothesis test?" is not an important question to ask when performing a hypothesis test.

Accepted Answer

Understanding the conclusions and interpretations of a hypothesis test is crucial as it helps determine the implications of the test results and guides decision-making based on statistical evidence.

Question 8

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 5% level of
significance.

Accepted Answer

The null hypothesis is that the mean power consumption is 250 W. The sample mean is 257.3 W, with a standard deviation of 15 W and a sample size of 20. Using a z-test, the calculated z-value is greater than the critical z-value at a 5% significance level, leading to the rejection of the null hypothesis.

Question 9

True or False: "Is the intended sample size large enough to achieve the desired power of the test
for the level of significance chosen?" should be among the questions asked when performing a
hypothesis test

Accepted Answer

Determining if the sample size is sufficient to achieve the desired power is crucial in hypothesis testing to ensure reliable and valid results.

Question 10

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the value of

Accepted Answer

The answer of SCENARIO 9-2
A student claims that he can...

Question 11

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-Referring to Scenario 9-3, the parameter of interest is

Accepted Answer

The parameter of interest is the mean power consumption of all such microwave ovens, as the manufacturer's claim is about the mean power consumption of all compact microwave ovens, not just this specific sample of 20.

Question 12

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the power of the test?

Accepted Answer

The power of the test is the probability of correctly rejecting the null hypothesis when the alternative is true. In this case, the alternative hypothesis is that the person is an agriculture major. The probability of correctly identifying an agriculture major is 1 - the probability of incorrectly identifying an agriculture major as a business major, which is 1 - 0.16 = 0.84. Therefore, the power of the test is 0.84.

Question 13

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the value of

Accepted Answer

The answer of SCENARIO 9-2
A student claims that he can...

Question 14

True or False: In instances in which there is insufficient evidence to reject the null hypothesis,
you must make it clear that this does not prove that the null hypothesis is true.

Accepted Answer

In hypothesis testing, failing to reject the null hypothesis means there is not enough evidence against it, but it does not confirm its truth.

Question 15

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what would be a Type II error?

Accepted Answer

A Type II error is failing to reject a null hypothesis that is false. In this case, it would be failing to identify the person as an agriculture major when they actually are an agriculture major.

Question 16

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-Referring to Scenario 9-3, for a test with a level of significance of 0.05, the critical value would
be ________.

Accepted Answer

The answer of SCENARIO 9-3
An appliance manufacturer claims to have...

Question 17

True or False: In instances in which there is insufficient evidence to reject the null hypothesis,
you must make it clear that this has proven that the null hypothesis is true.

Accepted Answer

Failing to reject the null hypothesis does not prove it is true; it only indicates that there is not enough evidence to support the alternative hypothesis.

Question 18

SCENARIO 9-3
An appliance manufacturer claims to have developed a compact microwave oven that consumes a
mean of no more than 250 W.From previous studies, it is believed that power consumption for
microwave ovens is normally distributed with a population standard deviation of 15 W.A consumer
group has decided to try to discover if the claim appears true.They take a sample of 20 microwave
ovens and find that they consume a mean of 257.3 W.
-Referring to Scenario 9-3, the population of interest is

Accepted Answer

The population of interest is the power consumption in all such microwave ovens, as the goal is to determine if the claim that the mean power consumption is no more than 250 W holds true for all microwave ovens, not just the 20 in the sample.

Question 19

SCENARIO 9-2
A student claims that he can correctly identify whether a person is a business major or an agriculture
major by the way the person dresses.Suppose in actuality that if someone is a business major, he can
correctly identify that person as a business major 87% of the time.When a person is an agriculture
major, the student will incorrectly identify that person as a business major 16% of the time.Presented
with one person and asked to identify the major of this person (who is either a business or an
agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the
person is a business major and the alternative that the person is an agriculture major.
-Referring to Scenario 9-2, what is the "actual confidence coefficient"?

Accepted Answer

The "actual confidence coefficient" refers to the probability of correctly identifying a true condition under the null hypothesis. Since the null hypothesis is that the person is a business major, and the student can correctly identify a business major 87% of the time, the actual confidence coefficient is 0.87.

Question 20

True or False: In conducting research, you should document both good and bad results.

Accepted Answer

Documenting both good and bad results is essential in research as it provides a comprehensive understanding of the study, helps identify areas for improvement, and ensures transparency and reproducibility.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests

True or False: You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

True or False: "What conclusions and interpretations can you reach from the results of the hypothesis test?" is not an important question to ask when performing a hypothesis test.

True or False: "Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test

True or False: In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this does not prove that the null hypothesis is true.

True or False: In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this has proven that the null hypothesis is true.

True or False: In conducting research, you should document both good and bad results.