Deck 26: The Power of a Test

Question 1

True or False: For a given level of significance,if the sample size is increased but the summary statistics remain the same,the probability of committing a Type II error will increase.

Answer 1

False

Question 2

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05,the probability of the operations manager failing to stop the process when the process is not working properly is ________ if the population mean bulb life is 490 hours.

Answer 2

0.3612

Question 3

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10,the power of the test is ________ if the population mean bulb life is 490 hours.

Answer 3

0.7638

Question 4

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01,the probability of the operations manager stopping the process if the population mean bulb life is 490 hours is ________.

Question 5

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the power of the test is ________ if the mean power consumption of all such microwave ovens is in fact 248 W.

Question 6

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10,the probability of a Type II error is ________ if the population mean bulb life is 490 hours.

Question 7

True or False: For a given level of significance,if the sample size is increased but the summary statistics remain the same,the probability of committing a Type I error will increase.

Question 8

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the probability of making a Type II error is ________ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Question 9

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01,the probability of the operations manager incorrectly stopping the process if the population mean bulb life is 510 hours is ________.

Question 10

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01,the probability of the operations manager failing to stop the process if the population mean bulb life is 490 hours is ________.

Question 11

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05,the probability of the operations manager not stopping the process when the process is in fact working properly is in fact below 500 hours is ________.

Question 12

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05,the probability of the operations manager stopping the process when the process is not working properly is ________ if the population mean bulb life is 490 hours.

Question 13

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10,the probability of a Type I error is ________ if the population mean bulb life is 510 hours.

Question 14

If we are performing a two-tail test of whether μ = 100,the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

A)less than
B)greater than
C)equal to
D)not comparable to

Question 15

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01,the probability of the operations manager not stopping the process if the population mean bulb life is 510 hours is ________.

Question 16

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05,the probability of the operations manager incorrectly stopping the process when the process is in fact working properly is ________.

Question 17

True or False: For a given sample size,the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

Question 18

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the power of the test is ________ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Question 19

True or False: For a given level of significance,if the sample size is increased but the summary statistics remain the same,the power of the test will increase.

Question 20

TABLE 9-10
A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience,the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.
Referring to Table 9-10,if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10,the confidence coefficient of the test is ________ if the population mean bulb life is 510 hours.

Question 21

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.1,the probability of a Type I error is ________ if the population mean effective time is 8 minutes.

Question 22

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.01,the probability of the company failing to market the new local anesthetic when its population mean effective time is greater than the 7.4 minutes is ________ if the population mean effective time is 8 minutes.

Question 23

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10,the power of the test is ________ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Question 24

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.1,the probability of a Type II error is ________ if the population mean effective time is 8 minutes.

Question 25

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10,the probability of making a Type II error is ________ if the mean power consumption of all such microwave ovens is in fact 248 W.

Question 26

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.01,the probability of making a Type II error is ________ if the mean power consumption of all such microwave ovens is in fact 248 W.

Question 27

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.05,the probability of the company not marketing the new local anesthetic when it is not better is ________.

Question 28

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.01,the probability of the company marketing the new local anesthetic when its population mean effective time is greater than the 7.4 minutes is ________ if the population mean effective time is 8 minutes.

Question 29

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.01,the power of the test is ________ if the mean power consumption of all such microwave ovens is in fact 248 W.

Question 30

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.1,the confidence coefficient of the test is ________ if the population mean effective time is 8 minutes.

Question 31

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.05,the probability of the company marketing the new local anesthetic when it is better is ________ if the population mean effective time is 8 minutes.

Question 32

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.05,the probability of the company incorrectly marketing the new local anesthetic when it is not better is ________.

Question 33

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.01,the probability of the company incorrectly marketing the new local anesthetic when its population mean effective time is not greater than the 7.4 minutes is ________.

Question 34

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.01,the power of the test is ________ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Question 35

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05,the probability of making a Type II error is ________ if the mean power consumption of all such microwave ovens is in fact 248 W.

Question 36

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10,the power of the test is ________ if the mean power consumption of all such microwave ovens is in fact 248 W.

Question 37

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.1,the power of the test is ________ if the population mean effective time is 8 minutes.

Question 38

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.10,the probability of making a Type II error is ________ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Question 39

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.05,the probability of the company failing to market the new local anesthetic when it is better is ________ if the population mean effective time is 8 minutes.

Question 40

TABLE 9-11
An appliance manufacturer claims to have developed a compact microwave oven that consumes a population 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.If there is evidence that the population mean consumption is greater than 250 W,the manufacturer will be unable to make the claim.
Referring to Table 9-11,if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.01,the probability of making a Type II error is ________ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

Question 41

TABLE 9-12
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.The company will market the new local anesthetic as being better if there is evidence that the population mean effective time is greater than the 7.4 minutes of the current local anesthetic.
Referring to Table 9-12,if you select a sample of 25 new local anesthetics and are willing to have a level of significance of 0.01,the probability of the company not marketing the new local anesthetic when its population mean effective time is not greater than the 7.4 minutes is ________.