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

The power of a statistical test is

SCENARIO 9-10 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager failing to stop the process when the process is not working properly is _____ if the population mean bulb life is 490 hours.

SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Scenario 9-8, state the null hypothesis for this study.

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.Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years.What is the p-value associated with the test statistic?

"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.

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 you reject the null hypothesis.What conclusion can you reach?

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

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

SCENARIO 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 (i.e.if there is evidence that the population proportion of "like the ads a lot" for the company's ads is less than 0.22)at a 0.01 level of significance. -Referring to Scenario 9-7, the value of is 0.90.

SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers.This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site.The conversion rate for a company's website was 10.1%.The website at the company was redesigned in an attempt to increase its conversion rates.A sample of 200 browsers at the redesigned site was selected.Suppose that 24 browsers made a purchase.The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance. -Referring to Scenario 9-8, the null hypothesis will be rejected if the test statistic is

SCENARIO 9-10 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager incorrectly stopping the process when the process is in fact working properly is _____.

The symbol for the probability of committing a Type I error of a statistical test is

SCENARIO 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 Scenario 9-5, the bank can conclude that the mean age is greater than 45 at a significance level of = 0.01.

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

In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this does not prove that the null hypothesis is true.

SCENARIO 9-6 The quality control engineer for a furniture manufacturer is interested in the mean amount of force in pounds necessary to produce cracks in stressed oak furniture.She performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650 pounds.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 Scenario 9-6, if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

SCENARIO 9-10 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly.Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed.The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours. -Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager not stopping the process when the process is in fact working properly is in fact below 500 hours is _____.

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

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.