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

Instruction 9-2 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park. A biologist wants to know if the mean number of parasites per butterfly is greater than 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies: $n = 46$ ; Arithmetic Mean $= 28.00$ ; Standard Deviation $= 25.92$ ; Standard Error $= 3.82$ ; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-2,the power of the test is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

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

Instruction 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 Instruction 9-3,what is the probability of making a Type II error if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.10 level of significance?

Instruction 9-1 A student claims that she can correctly identify whether a person is studying a business or science major by the way the person dresses. Suppose in actuality that if someone is studying a business major, she can correctly identify that person as a business student 87% of the time. When a person is studying a science major, the student will incorrectly identify that person as a business student 16% of the time. Presented with one person and asked to identify the area of study of this person (who is studying either a business or science major), she considers this to be a hypothesis test with the null hypothesis being that the person is a business student and the alternative that the person is a science student. -Referring to Instruction 9-1,what would be a Type II error?

A major DVD rental chain is considering opening a new store in an area that currently does not have any such stores.The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area own DVD players.It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. -State the test of hypothesis that is of interest to the rental chain.

Instruction 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. -Referring to Instruction 9-5,if the same sample was used to test the opposite one-tailed test,what would be that test's p-value?

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.

Instruction 9-7 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park. A biologist wants to know if the mean number of parasites per butterfly is greater than 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies: $n = 46$ ; Arithmetic Mean $= 28.00$ ; Standard Deviation $= 25.92$ ; Standard Error $= 3.82$ ; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -True of False: Referring to Instruction 9-7,the biologist can conclude that there is sufficient evidence to show that the mean number of parasites per butterfly is greater than 20 using a level of significance of 0.10.

"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.

Suppose,in testing a hypothesis about a proportion,the p-value is computed to be 0.034.The null hypothesis should be rejected if the chosen level of significance is 0.01.

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90,a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin.The value of the test statistic in this problem is approximately equal to

Instruction 9-2 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park. A biologist wants to know if the mean number of parasites per butterfly is greater than 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies: $n = 46$ ; Arithmetic Mean $= 28.00$ ; Standard Deviation $= 25.92$ ; Standard Error $= 3.82$ ; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-2,the probability of committing a Type II error is ________ if the mean number of parasites per butterfly on Blue Tiger butterflies in Kakadu National Park is 18 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

Instruction 9-7 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park. A biologist wants to know if the mean number of parasites per butterfly is greater than 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies: $n = 46$ ; Arithmetic Mean $= 28.00$ ; Standard Deviation $= 25.92$ ; Standard Error $= 3.82$ ; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-7,if these data were used to perform a two-tailed test,the p-value would be 0.042.

Instruction 9-7 Microsoft Excel was used on a set of data involving the number of parasites found in a random sample of 46 Blue Tiger butterflies captured in Kakadu National Park. A biologist wants to know if the mean number of parasites per butterfly is greater than 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 butterflies: $n = 46$ ; Arithmetic Mean $= 28.00$ ; Standard Deviation $= 25.92$ ; Standard Error $= 3.82$ ; Null Hypothesis: $H _ { 0 } : \mu \leq 20.000 ; a = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic $= 2.09$ ; One-Tailed Test Upper CriticalValue $= 1.3006 ; p$ value $= 0.021$ ; Decision $=$ Reject. -Referring to Instruction 9-7,the parameter the biologist is interested in is the

If a researcher rejects a false null hypothesis,she has made a ________ decision.

Instruction 9-4 A drug company is considering marketing a new local anaesthetic. The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anaesthetic; otherwise, it will continue to produce the older drug. 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 Instruction 9-4,the p-value of the test is ________

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the average number of tissues used during a cold.Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: $\bar { X }$ = 52,s = 22. - Using the sample information provided,calculate the value of the test statistic.

Which of the following would be an appropriate alternative hypothesis?

Instruction 9-4 A drug company is considering marketing a new local anaesthetic. The effective time of the anaesthetic 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 anaesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anaesthetic; otherwise, it will continue to produce the older drug. 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 Instruction 9-4,what is the power of the test if the mean effective time of the anaesthetic is 7.5 using a 0.10 level of significance?

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club.She would now like to determine whether or not the mean age of her customers is greater than 30.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. -If she wants to have a level of significance at 0.01,what decision should she make?