Question 1

TABLE 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 Table 9.3,the value of the test statistic is ________.

Accepted Answer

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

Question 2

TABLE 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 Table 9-3,the null hypothesis will be rejected at 1% level of significance.

Accepted Answer

We need to perform a one-sample t-test to test the hypothesis about the population mean power consumption of the microwave ovens. From Table 9-3, we can find the critical t-value for a one-tailed test with 19 degrees of freedom (df = n-1, where n = 20) and a significance level of 1%, which is 2.539. 
Now, we can calculate the test statistic using the formula:
t = (sample mean - hypothesized population mean) / (sample standard error)
where hypothesized population mean is 250 W, sample mean is 257.3 W, and sample standard error is calculated as: standard deviation / sqrt(n) = 15 / sqrt(20) = 3.3541. 
Substituting the values, we get:
t = (257.3 - 250) / 3.3541 = 2.19
Since the calculated t-value (2.19) is less than the critical t-value (2.539), we fail to reject the null hypothesis at 1% level of significance. Therefore, the answer is B.

Question 3

TABLE 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 Table 9-3,the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are A)H₀ : μ = 250 versus H₁ : μ ≠ 250. B)H₀ : μ ≥ 250 versus H₁: μ < 250. C)H₀ : μ ≤ 250 versus H₁: μ > 250. D)H₀ : μ ≥ 257.3 versus H₁: μ < 257.3.

Accepted Answer

The appropriate null hypothesis is that the mean power consumption is less than or equal to 250 W, and the alternative hypothesis is that the mean power consumption is greater than 250 W. This is represented by the pair of hypotheses H₀ : μ ≤ 250 versus H₁: μ > 250. This is because the manufacturer's claim is that the mean power consumption is no more than 250 W, which is equivalent to saying that it is less than or equal to 250 W. The sample result of a mean power consumption of 257.3 W suggests that the manufacturer's claim may not be reasonable, and we want to test this at a significance level of 0.05. Therefore, we use a one-tailed test with a critical value of 1.645 (from the standard normal distribution table) and calculate the test statistic as (257.3 - 250) / (15 / sqrt(20)) = 2.44. Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest that the mean power consumption is greater than 250 W.

Question 4

TABLE 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 Table 9-3,the null hypothesis will be rejected at 5% level of significance.

Accepted Answer

To determine if the null hypothesis will be rejected at a 5% level of significance, we need to perform a one-sample t-test using the formula:
t = (x̄ - μ) / (s / sqrt(n))
where x̄ is the sample mean, μ is the hypothesized population mean (in this case, 250 W), s is the sample standard deviation (which we can estimate using the population standard deviation of 15 W), and n is the sample size (20).

Using the values given in the problem, we get:
t = (257.3 - 250) / (15 / sqrt(20)) = 1.71

Using the t-distribution table with 19 degrees of freedom (n-1), and a two-tailed test at a 5% level of significance, we find the critical value to be ±2.093. Since our calculated t-value of 1.71 is within the range of -2.093 to +2.093, we fail to reject the null hypothesis.

Therefore, the answer is false. We cannot reject the claim that the compact microwave oven consumes a mean of no more than 250 W at a 5% level of significance.

Question 5

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Table 9-4,the value of the test statistic is ________.

Accepted Answer

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

Question 6

TABLE 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 Table 9-3,the p-value of the test is ________.

Accepted Answer

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

Question 7

TABLE 9-5
A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45 years,versus an alternative that the mean age is greater than 45 years.They take a sample and calculate a p-value of 0.0202.
-True or False: Referring to Table 9-5,the null hypothesis would be rejected at a significance level of α = 0.05.

Accepted Answer

Looking at Table 9-5, we see that the critical value for a one-tailed test at α = 0.05 is 1.645. Since the calculated p-value (0.0202) is less than the significance level of 0.05 and falls in the rejection region (p-value < α/2), we reject the null hypothesis. Therefore, the answer is A) True.

Question 8

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision. -Referring to Table 9-4,the appropriate hypotheses are A)H₀: μ = 7.4 versus H₁ : μ ≠ 7.4. B)H₀: μ ≤ 7.4 versus H₁ : μ > 7.4. C)H₀ : μ ≥ 7.4 versus H₁ : μ < 7.4. D)H₀ : μ > 7.4 versus H₁:μ ≤ 7.4.

Accepted Answer

The company wants to market the new anesthetic only if the mean effective time is lower than 7.4 minutes. Therefore, the null hypothesis should be that the mean is greater than or equal to 7.4, and the alternative hypothesis should be that the mean is less than 7.4.

Question 9

TABLE 9-5
A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45 years,versus an alternative that the mean age is greater than 45 years.They take a sample and calculate a p-value of 0.0202.
-True or False: Referring to Table 9-5,the bank can conclude that the mean age is greater than 45 at a significance level of α = 0.01.

Accepted Answer

The p-value of 0.0202 is greater than the significance level of α = 0.01, so the bank cannot reject the null hypothesis at this level.

Question 10

TABLE 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 Table 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 in this scenario is not just the sample of 20 microwave ovens, but rather all microwave ovens. The consumer group wants to determine if the manufacturer's claim is true for all such microwave ovens, not just the ones they sampled. Therefore, the population of interest is the power consumption in all such microwave ovens, making choice B the best answer.

Question 11

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-True or False: Referring to Table 9-4,if the level of significance had been chosen as 0.05,the company would market the new anesthetic.

Accepted Answer

The table is not provided, so the critical value or p-value cannot be determined. Therefore, it cannot be determined whether the null hypothesis would be rejected or not, and thus cannot determine whether the company would market the new anesthetic or not.

Question 12

TABLE 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 Table 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 consumer group can perform a hypothesis test with the null hypothesis that the mean power consumption is 250 W. Given the sample mean of 257.3 W, a standard deviation of 15 W, and a sample size of 20, they can calculate the test statistic and compare it to the critical value for a 5% significance level. If the test statistic exceeds the critical value, they can reject the null hypothesis, suggesting there is enough evidence against the manufacturer's claim.

Question 13

TABLE 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 Table 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 test assumptions include the requirement that the population from which the sample is drawn should have a normal distribution. In this case, the assumption is that the power consumption for microwave ovens is normally distributed, and this assumption must hold for the test to be valid.

Question 14

TABLE 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 Table 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, as we are trying to see if the manufacturer's claim (that the mean consumption is no more than 250 W) applies to all ovens, not just the sample we have.

Question 15

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-True or False: Referring to Table 9-4,if the level of significance had been chosen as 0.05,the null hypothesis would be rejected.

Accepted Answer

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

Question 16

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Table 9-4,the p-value of the test is ________.

Accepted Answer

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

Question 17

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-Referring to Table 9-4,for a test with a level of significance of 0.10,the critical value would be ________.

Accepted Answer

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

Question 18

TABLE 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 a 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 size of 36 results in a sample mean of 7.1.A hypothesis test will be done to help make the decision.
-True or False: Referring to Table 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 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 is 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 19

TABLE 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 Table 9-3,for a test with a level of significance of 0.05,the critical value would be ________.

Accepted Answer

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

Question 20

TABLE 9-5
A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45 years,versus an alternative that the mean age is greater than 45 years.They take a sample and calculate a p-value of 0.0202.
-True or False: Referring to Table 9-5,the null hypothesis would be rejected at a significance level of α = 0.01.

Accepted Answer

The null hypothesis would not be rejected at a significance level of α = 0.01 because the p-value (0.0202) is greater than 0.01.

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