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

Instruction 9-1 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: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

Instruction 9-1 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: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,the biologist can conclude that there is sufficient evidence to show that the mean number of parasites per butterfly is greater than 20 with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

If you know that the level of significance (α)of a test is 5%,you can tell that the probability of committing a Type II error (β)is

Which of the following statements is NOT true about the level of significance in a hypothesis test?

Instruction 9-7 A major home improvement store conducted its biggest brand recognition campaign in the company's history.A series of new television advertisements featuring well-known entertainers and sports figures were launched.A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot".A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot".The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%.Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance. -Referring to Instruction 9-7,state the alternative hypothesis for this study.

Instruction 9-7 A major home improvement store conducted its biggest brand recognition campaign in the company's history.A series of new television advertisements featuring well-known entertainers and sports figures were launched.A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot".A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot".The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%.Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance. -Referring to Instruction 9-7,the company officials can conclude that there is sufficient evidence to show that the series of television advertisements are less successful than the typical ad using a level of significance of 0.05.

Instruction 9-6 The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture.She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650.The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test. -Referring to Instruction 9-6,if the test is performed with a level of significance of 0.10,the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

Instruction 9-1 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: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,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 9-4 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 probability of making a Type II error if the mean effective time of the anaesthetic is 7.5 using a 0.10 level of significance?

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,if the level of significance had been chosen as 0.05,the null hypothesis would be rejected.

If the Type I error (α)for a given test is to be decreased,then for a fixed sample size n

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,the bank can conclude that the average age is greater than 45 at a significance level of α = 0.01.

Instruction 9-1 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: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,the parameter the biologist is interested in is the

Instruction 9-1 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: $H _ { 0 } : \mu \leq 20.000 ; \alpha = 0.10 ; \mathrm { df } = 45 ; T$ Test Statistic = 2.09; One-Tailed Test Upper Critical Value $= 1.3006 ; p$ -value $= 0.021 ;$ Decision $=$ Reject. -Referring to Instruction 9-1,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 30 using a 0.1 level of significance and assuming that the population standard deviation is 25.92.

If all else remains equal,which of the following will increase the power of a t test?

Instruction 9-7 A major home improvement store conducted its biggest brand recognition campaign in the company's history.A series of new television advertisements featuring well-known entertainers and sports figures were launched.A key metric for the success of television advertisements is the proportion of viewers who "like the ads a lot".A study of 1,189 adults who viewed the ads reported that 230 indicated that they "like the ads a lot".The percentage of a typical television advertisement receiving the "like the ads a lot" score is believed to be 22%.Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad at a 0.01 level of significance. -Referring to Instruction 9-7,the company officials can conclude that there is sufficient evidence to show that the series of television advertisements are less successful than the typical ad using a level of significance of 0.01.

For a given level of significance,if the sample size is increased,the probability of committing a Type I error will increase.

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,the null hypothesis would be rejected at a significance level of α = 0.05.

Instruction 9-2 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 9-2,what would be a Type I error?

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 248 W using a 0.10 level of significance?