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

SCENARIO 9-4 A drug company is considering marketing a new local anesthetic.The effective time of the anesthetic 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 anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower.If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one.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 Scenario 9-4, the appropriate hypotheses are:

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 thealternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.10.

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, what will be the p-value if these data were used to perform a two-tail test?

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 0.01, the probability of the operations manager not stopping the process if the population mean bulb life is 510 hours is .

If the Type I error ( $\alpha$ ) for a given test is to be decreased, then for a fixed sample size n

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, if the same sample was used to test the opposite one-tail test, what would be that test's p-value?

SCENARIO 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-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, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650 pounds..Then 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 mean family income in a community exceeds $50,000

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 II error will increase.

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

For a given sample size n, if the level of significance ( $\alpha$ ) is decreased, the power of the test

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years, but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, if these data were used to perform a two-tail test, the p-value would be 0.1254.

The symbol for the confidence coefficient 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 0.10, the probability of a Type I error is if the population mean bulb life is 510 hours.

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

The smaller the p-value, the stronger is the evidence against the null hypothesis.

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.

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

True or False With a test being robust, it does not lose power when the shape of the population distribution departs from a normal distribution.

SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years, but their mean SAT score is lower than previous years.He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53.The university's record indicates that the mean SAT score for entering students from previous years is 1,520.He wants to find out if his claim is supported by the evidence at a 5% level of significance. -Referring to Scenario 9-9, the president can conclude that the mean SAT score of the entering class this year is lower than previous years using a level of significance of 0.10.