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

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

If a researcher rejects a true null hypothesis,she has made a ________ 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 power of the test if the mean power consumption of all such microwave ovens is in fact 257.3 W using a 0.10 level of significance?

The symbol for the power of a statistical test is

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,state the alternative hypothesis for this study.

The larger is the p-value,the more likely one is to reject the null hypothesis.

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 critical value should the biologist use to determine the rejection region?

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

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

If a researcher accepts a true null hypothesis,she has made a ________decision.

The symbol for the level of significance of a statistical test is

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,what critical value should the company officials use to determine the rejection region?

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

Suppose,in testing a hypothesis about a proportion,the p-value is computed to be 0.043.The null hypothesis should be rejected if the chosen level of significance is 0.05.

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

For an experiment,the probability of a Type I error is 0.05 and the probability of a Type II error is 0.20.The power of the test is

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.Then if the test is performed with a level of significance of 0.10,the null hypothesis would be rejected.

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 0.05 level of significance?

If a test of hypothesis has a Type I error probability (α)of 0.01,it means that

Suppose,in testing a hypothesis about a proportion,the Z test statistic is computed to be 2.04.The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.