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

A proper methodology in performing hypothesis tests is to ask whether a random sample can be selected from the population of interest.

Suppose we wish to test H₀: μ ≤ 47 versus H₁: μ > 47.What will result if we conclude that the mean is greater than 47 when its true value is really 52?

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 9-6 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,suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650.What would be the p-value of this one-tailed test?

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,the null hypothesis will be rejected at 1% level of significance.

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 0.05 level of significance and assuming that the population standard deviation is 25.92.

Instruction 9-9 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 9-9,the parameter the company officials is interested in is

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.

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. - Suppose the alternative we wanted to test was H₁: $\mu$ < 60.State the correct rejection region for $\alpha$ = 0.05.

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 null hypothesis would be rejected if a 5% probability of committing a Type I error is allowed.

The power of a statistical test is

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 power of the test if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.05 level of significance?

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,the parameter of interest is

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. -The appropriate hypotheses to test are

Instruction 9-8 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 9-8,the largest level of significance at which the null hypothesis will not be rejected is ______.

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,the consumer group can conclude that there is enough evidence to prove that the manufacturer's claim is not true when allowing for a 5% probability of committing a Type I error.

If,as a result of a hypothesis test,you reject the null hypothesis when it is false,then you have committed

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 is the value of β?

Instruction 9-9 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 9-9,state the null hypothesis for this study.

Using a set of data more than once for inference or selecting a model is known as________.