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

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 accepted at a level of significance of 0.01.

The symbol for the confidence coefficient of a statistical test is

The value that separates a rejection region from a non-rejection region is called the ________.

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 0.05,the null hypothesis would be rejected.

If an economist wishes to determine whether there is evidence that average family income in a community exceeds $50,000

An entrepreneur is considering the purchase of a coin-operated laundry.The current owner claims that over the past five years,the average daily revenue was $675 with a standard deviation of $75.A sample of 30 days reveals a daily average revenue of $625.If you were to test the null hypothesis that the daily average revenue was $675,which test would you use?

In conducting research,you should document both good and bad results.

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?

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 rental chain's conclusion from the hypothesis test using a 5% level of significance is

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 power of the test?

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 5% probability of committing a Type I error is allowed.

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

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 0.05 level of significance?

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 β?

You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

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 = 0.01.

A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75.An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65.If you wanted to test whether the mean balance is different from $75 and decided to reject the null hypothesis,what conclusion could you reach?

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.

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 lowest level of significance at which the null hypothesis can be rejected is ________.

Which of the following would be an appropriate null hypothesis?