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.
-Referring to Scenario 9-3,the parameter of interest is
A)the mean power consumption of the 20 microwave ovens.
B)the mean power consumption of all such microwave ovens.
C)250
D)257.3

Accepted Answer

The parameter of interest is the mean power consumption of all such microwave ovens, which is unknown. The manufacturer claims that this mean is no more than 250 W. The sample mean of 257.3 W suggests that the claim may not be true, but we cannot conclude anything without performing a hypothesis test and calculating a p-value. Therefore, the best choice is B, as we are interested in the mean power consumption of all microwave ovens, not just the 20 sampled ones.

Question 2

Referring to Scenario 9-3,the consumer group can conclude that there is enough evidence that the manufacturer's claim is not true when allowing for a 5% probability of committing a Type I error.

Accepted Answer

The p-value of the hypothesis test is less than the significance level of 0.05, which means that the null hypothesis is rejected. Therefore, there is enough evidence to conclude that the manufacturer's claim is not true. When allowing for a 5% probability of committing a Type I error, this conclusion is still valid.

Question 3

SCENARIO 9-4
A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of
7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Scenario 9-4,for a test with a level of significance of 0.10,the critical value would be .

Accepted Answer

The answer of SCENARIO 9-4
A drug company is considering marketing...

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 is the power of the test?
A)0.13
B)0.16
C)0.84
D)0.87

Accepted Answer

The power of the test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, the alternative hypothesis is that the person is an agriculture major. The power of the test can be calculated using the formula:

power = 1 - P(type II error)

where P(type II error) is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. Since the student incorrectly identifies an agriculture major as a business major with a probability of 0.16, the probability of correctly identifying an agriculture major is 1 - 0.16 = 0.84. Therefore, the power of the test is 0.84.

Question 5

Referring to Scenario 9-3,the p-value of the test is .

Accepted Answer

The answer of Referring to Scenario 9-3,the p-value of the...

Question 6

SCENARIO 9-4
A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of
7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Scenario 9-4,the null hypothesis will be rejected with a level of significance of 0.10.

Accepted Answer

The null hypothesis is that the mean effective time of the new anesthetic is equal to 7.4 minutes. With a sample mean of 7.1, a sample size of 36, and a standard deviation of 1.2, the test statistic can be calculated. At a significance level of 0.10, the null hypothesis will be rejected if the test statistic falls in the critical region, which it does in this case.

Question 7

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 central limit theorem states that the distribution of sample means will be approximately normal, regardless of the shape of the population distribution, if the sample size is large enough. In this case, the sample size is 30, which is large enough to invoke the central limit theorem. Therefore, the power consumption for microwave ovens can be assumed to have a normal distribution, and the test is valid.

Question 8

Referring to Scenario 9-3,the null hypothesis will be rejected at 5% level of significance.

Accepted Answer

The null hypothesis is rejected when the p-value is less than the level of significance. In this case, the p-value is 0.04, which is less than the level of significance of 0.05. Therefore, the null hypothesis is rejected at the 5% level of significance.

Question 9

SCENARIO 9-4 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of 7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision. -Referring to Scenario 9-4,the appropriate hypotheses are: A)H ₀: $\mu$ = 7.4 versus H₁: $\mu$ $\neq$ 7.4 B)H ₀: $\mu$ $\le$ 7.4 versus H₁: $\mu$ $\gt$ 7.4 C)H ₀: $\mu$ $\ge$ 7.4 versus H₁: $\mu$ $\lt$ 7.4 D)H ₀: $\mu$ $\gt$ 7.4 versus H₁: $\mu$ $\le$ 7.4

Accepted Answer

The null hypothesis (H0) should state that the mean effective time of the new anesthetic is greater than or equal to 7.4 minutes (the mean effective time of the current anesthetic), and the alternative hypothesis (H1) should state that the mean effective time of the new anesthetic is less than 7.4 minutes, as the company is interested in marketing the new anesthetic only if its mean effective time is lower.

Question 10

SCENARIO 9-4
A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of
7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Scenario 9-4,the p-value of the test is .

Accepted Answer

The answer of SCENARIO 9-4
A drug company is considering marketing...

Question 11

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 ?
A)0.13
B)0.16
C)0.84
D)0.87

Accepted Answer

The value of 0.13 represents the probability of a Type I error, which is the probability of incorrectly rejecting the null hypothesis when it is true. In this scenario, it is the probability of incorrectly identifying a business major as an agriculture major.

Question 12

SCENARIO 9-4
A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of
7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Scenario 9-4,the value of the test statistic is .

Accepted Answer

The answer of SCENARIO 9-4
A drug company is considering marketing...

Question 13

SCENARIO 9-4
A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of
7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Scenario 9-4,if the level of significance had been chosen as 0.05,the null hypothesis would be rejected.

Accepted Answer

We cannot determine whether the null hypothesis would be rejected or not without calculating the test statistic and comparing it to the critical value.

Question 14

Referring to Scenario 9-3,the null hypothesis will be rejected at 1% level of significance.

Accepted Answer

The scenario is not provided, so it is impossible to determine whether or not the null hypothesis will be rejected at a 1% level of significance.

Question 15

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 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,the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are: A)H ₀: $\mu$= 250 versus H₁: $\mu$ $\neq$250 B)H ₀: $\mu$ $\ge$ 250 versus H₁: $\mu$ $\lt$ 250 C)H ₀: $\mu$$\le$ 250 versus H₁: $\mu$ $\gt$ 250 D)H ₀: $\mu$ $\ge$ 257.3 versus H₁: $\mu$ $\lt$ 257.3

Accepted Answer

The null hypothesis (H0) should state the manufacturer's claim as true, which is that the mean power consumption is no more than 250 W ($\mu \leq 250$). The alternative hypothesis (H1) is what the consumer group is trying to prove, which is that the mean power consumption is greater than 250 W ($\mu > 250$).

Question 17

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
A)the power consumption in the 20 microwave ovens.
B)the power consumption in all such microwave ovens.
C)the mean power consumption in the 20 microwave ovens.
D)the mean power consumption in all such microwave ovens.

Accepted Answer

The population of interest refers to the entire group about which the manufacturer is making a claim, which in this case is all such microwave ovens, not just the sample of 20.

Question 18

Referring to Table 9.3,the value of the test statistic is .

Accepted Answer

The answer of Referring to Table 9.3,the value of the...

Question 19

SCENARIO 9-4
A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic the drug company is currently producing has a normal distribution with an mean of
7.4 minutes with a standard deviation of 1.2 minutes.The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation,but the mean effective time may be lower.If it is lower,the drug company will market the new anesthetic;otherwise,they will continue to produce the older one.A sample of size 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Scenario 9-4,if the level of significance had been chosen as 0.05,the company would market the new anesthetic.

Accepted Answer

We need to conduct a hypothesis test to make a conclusion about whether the new anesthetic has a lower mean effective time or not. We do not have enough information to make a decision solely based on the sample mean and level of significance.

Question 20

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 $\beta$ ?
A)0.13
B)0.16
C)0.84
D)0.87

Accepted Answer

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

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

Referring to Scenario 9-3,the consumer group can conclude that there is enough evidence that the manufacturer's claim is not true when allowing for a 5% probability of committing a Type I error.

Referring to Scenario 9-3,the p-value of the test is .

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.

Referring to Scenario 9-3,the null hypothesis will be rejected at 5% level of significance.

Referring to Scenario 9-3,the null hypothesis will be rejected at 1% level of significance.

Referring to Table 9.3,the value of the test statistic is .