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

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 248 W using a 0.05 level of significance?

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 was selected.Suppose that the test statistic is -2.20.Can we conclude that H₀ should be rejected at the (a)α = 0.10, (b)α = 0.05,and (c)α = 0.01 level of Type I 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.The decision on the hypothesis test using a 5% level of significance is

Which of the following would be an appropriate null hypothesis?

The test statistic measures how close the computed sample statistic has come to the hypothesised population parameter.

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

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 is the "actual level of significance" of the test?

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 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 is the value of α?

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 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.

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 null hypothesis for this study.

You have created a 95% confidence interval for μ with the result (10,15).What decision will you make if you test H₀: μ = 16 versus H₁: μ ≠ 16 at α = 0.01?

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 0.05 level of significance?

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.

The power of a test is measured by its capability of

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?

The power of a test is defined as 1 - α.

A sample is used to obtain a 95% confidence interval for the mean of a population.The confidence interval goes from 15 to 19.If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20,the null hypothesis could be rejected at a level of significance of 0.05.

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.