Exam 9: Introduction to Hypothesis Testing

Generally,it is possible to appropriately test a null and alternative hypotheses using the test statistic approach and reach a different conclusion than would be reached if the p-value approach were used.

The Adams Shoe Company believes that the mean size for men's shoes is now more than 10 inches.To test this,it has selected a random sample of n = 100 men.Assuming that the test is to be conducted using a .05 level of significance,a p-value of .07 would lead the company to conclude that its belief is correct.

For the following hypothesis test: With n = 80,σ = 9,and = 47.1,state the conclusion.

Whenever possible,in establishing the null and alternative hypotheses,the research hypothesis should be made the alternative hypothesis.

The National Club Association does periodic studies on issues important to its membership.The 2012 Executive Summary of the Club Managers Association of America reported that the average country club initiation fee was $31,912.Suppose a random sample taken in 2009 of 12 country clubs produced the following initiation fees: Based on the sample information,can you conclude at the α = 0.05 level of significance that the average 2009 country club initiation fees are lower than the 2008 average? Conduct your test at the level of significance.

If a hypothesis test leads to incorrectly rejecting the null hypothesis,a Type II statistical error has been made.

A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.Based on this sample information,he decides if the desired standard is not being met.He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise.On one occasion where a sample of 40 customers was selected,the average number of days was 6.65,with a sample standard deviation of 1.5 days.Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this question.Conduct the test using this p-value.

According to CNN business partner Careerbuilder.com,the average starting salary for accounting graduates in 2008 was at least $47,413.Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2008. State the appropriate null and alternative hypotheses.

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces.Every box of cereal is not expected to contain exactly the targeted weight,but the average of all boxes filled should.At the end of every shift (eight hours),16 boxes are selected at random and the mean and standard deviation of the sample are computed.Based on these sample results,the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate.At the end of a particular shift during which the machine was filling 24-ounce boxes of Mini-Oats,the sample mean of 16 boxes was 24.32 ounces,with a standard deviation of 0.70 ounce.Assist the production control manager in determining if the machine is achieving its targeted average using test statistic and critical value t.Conduct the test using a p-value.

The produce manager for a large retail grocery store believes that an average head of lettuce weighs more than 1.7 pounds.If she were to test this statistically,what would the null and alternative hypotheses be and what is the research hypothesis?

Hypothesis testing and confidence interval estimation are essentially two totally different statistical procedures and share little in common with each other.

Waiters at Finegold's Restaurant and Lounge earn most of their income from tips.Each waiter is required to "tip-out" a portion of tips to the table bussers and hostesses.The manager has based the "tip-out" rate on the assumption that the mean tip is at least 15% of the customer bill.To make sure that this is the correct assumption,he has decided to conduct a test by randomly sampling 60 bills and recording the actual tips. Calculate the probability of a Type II error if the true mean is 14%.Assume that the population standard deviation is known to be 2% and that a significance level equal to 0.01 will be used to conduct the hypothesis test.

The makers of Mini-Oats Cereal have an automated packaging machine that can be set at any targeted fill level between 12 and 32 ounces.Every box of cereal is not expected to contain exactly the targeted weight,but the average of all boxes filled should.At the end of every shift (eight hours),16 boxes are selected at random and the mean and standard deviation of the sample are computed.Based on these sample results,the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate.Use α= 0.05.At the end of a particular shift during which the machine was filling 24-ounce boxes of Mini-Oats,the sample mean of 16 boxes was 24.32 ounces,with a standard deviation of 0.70 ounce.Assist the production control manager in determining if the machine is achieving its targeted average using test statistic and critical value t.

For testing a research hypothesis,the burden of proof that a new product is no better than the original is placed on the new product,and the research hypothesis is formulated as the null hypothesis.

A contract with a parts supplier calls for no more than .04 defects in the large shipment of parts.To test whether the shipment meets the contract,the receiving company has selected a random sample of n = 100 parts and found 6 defects.If the hypothesis test is to be conducted using a significance level equal to 0.05,what is the test statistic and what conclusion should the company reach based on the sample data?

If the sample data lead the decision maker to reject the null hypothesis,the alpha level is the maximum probability of committing a Type II error.

Because of the complex nature of the U.S.income tax system,many people have questions for the Internal Revenue Service (IRS).Yet,an article published by the Detroit Free Press entitled "Assistance: IRS Help Centers Give the Wrong Information" discusses the propensity of IRS staff employees to give incorrect tax information to tax-payers who call with questions.Then IRS Inspector General Pamela Gardiner told a Senate subcommittee that "the IRS employees at 400 taxpayer assistance centers nationwide encountered 8.5 million taxpayers face-to-face last year.The problem: When inspector general auditors posing as taxpayers asked them to answer tax questions,the answers were right 69% of the time." Suppose an independent commission was formed to test whether the 0.69 accuracy rate is correct or whether it is actually higher or lower.The commission has randomly selected n = 180 tax returns that were completed by IRS assistance employees and found that 105 of the returns were accurately completed. Using an α= 0.05 level,based on the sample data,what conclusion should be reached about the IRS rate of correct tax returns?

One of the factors that a company will use in determining whether it will locate a new facility in a community is the status of the real estate market.The managers believe that an important measure of the real estate market is the average length of time that homes stay on the market before selling.They believe that if the mean time on the market is less than 45 days,the real estate market is favorable.To test this in a particular area,a random sample of n = 100 homes that sold during the past six months was selected.The mean for this sample was 40 days.It is believed that the population standard deviation is 15 days.If the test is conducted using a 0.05 level of significance,what conclusion should be reached?

For the following hypothesis test With n = 100 and p = 0.66,state the calculated value of the test statistic.

Which of the following is not a required step in finding beta?