Exam 26: The Power of a Test

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.

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.

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.

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.

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.

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.

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 ________.

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 ________.

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 ________.

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.

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.

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.

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.

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.

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 ________.

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.

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.

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.

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 ________.

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.