Exam 11: Hypothesis Tests and Estimation for Population Variances

An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes.The correct null and alternative hypotheses for this test are:

Sample A has a sample size of 15 and a standard deviation of 4.Sample B has a sample size of 30 and a standard deviation of 6.Both samples were taken from the same population.The 95 percent confidence interval estimate for the standard deviation of the population based on sample A will be ________ that based on sample B.

One of the key quality characteristics in many service environments is that the variation in service time be reasonably small.Recently,a major amusement park company initiated a new line system at one of its parks.It then wished to compare this new system with the old system in place at a comparable park in another state.At issue is whether the standard deviation in waiting time is less under the new line system than under the old line system.The following information was collected: Assuming that it wishes to conduct the test using a 0.05 level of significance,the test statistic will be F = 1.5625.

Two airlines are being compared with respect to the time it takes them to turn a plane around from the time it lands until it takes off again.The study is interested in determining whether there is a difference in the variability between the two airlines.They wish to conduct the hypothesis test using an alpha = 0.02.If random samples of 20 flights are selected from each airline,what is the appropriate F critical value?

The managers for a vegetable canning facility claim the standard deviation for the ounces per can on the new automated line is less than for the older manual line.Given this,the correct null and alternative hypotheses for performing the statistical test are: .

The logic behind the F-test for testing whether two populations have equal variances is to determine whether sample variances computed from random samples selected from the two populations differ due to sampling error,or whether the difference is more than can be attributed to sampling error alone,in which case,we conclude that the populations have different variances.

There is interest at the American Savings and Loan as to whether there is a difference between average daily balances in checking accounts that are joint accounts (two or more members per account)versus single accounts (one member per account).To test this,a random sample of checking accounts was selected with the following results: Based upon these data,if tested using a significance level equal to 0.10,the assumption of equal population variances should be rejected.

In a hypothesis test involving two population variances,if the null hypothesis states that the two variances are strictly equal,then the test statistic is a chi-square statistic.

If a hypothesis test for a single population variance is to be conducted using a significance level of to 0.10,a sample size of n = 16,and the test is a one-tailed upper-tail test,the critical value is:

The Department of Weights and Measures in a southern state has the responsibility for making sure that all commercial weighing and measuring devices are working properly.For example,when a gasoline pump indicates that 1 gallon has been pumped,it is expected that 1 gallon of gasoline will actually have been pumped.The problem is that there is variation in the filling process.The state's standards call for the mean amount of gasoline to be 1.0 gallon with a standard deviation not to exceed 0.010 gallons.Recently,the department came to a gasoline station and filled 10 cans until the pump read 1.0 gallon.It then measured precisely the amount of gasoline in each can.The following data were recorded: Based on these data what should the Department of Weights and Measures conclude if it wishes to test whether the standard deviation exceeds 0.010 gallons or not,using a 0.05 level of significance?

When using a chi-square test for the variance of one population,we are assuming that the population is normally distributed.

A PC company uses two suppliers for rechargeable batteries for its notebook computers.Two factors are important quality features of the batteries: mean use time and variation.It is desirable that the mean use time be high and the variability be low.Recently,the PC maker conducted a test on batteries from the two suppliers.In the test,9 randomly selected batteries from Supplier 1 were tested and 12 randomly selected batteries from Supplier 2 were tested.The following results were observed: Based on these sample results,can the PC maker conclude that a difference exists between the two batteries with respect to the population mean use time? Test using a 0.10 level of significance.

The F test statistic for testing whether the variances of two populations are the same is always positive.

A manufacturer of industrial plywood has a contract to supply a boat maker with a large amount of plywood.One of the specifications calls for the standard deviation in thickness to not exceed .03 inches.A sample of n = 30 sheets was sampled randomly from a recent production run.The mean thickness was right at the 3/4 inch target thickness and the sample standard deviation was .05 inches.Testing at the 0.05 level of significance,which of the following is true?

The variance in the diameter of a bolt should not exceed 0.500 mm.A random sample of n = 12 bolts showed a sample variance of 0.505 mm.The test statistic is χ² = 11.11.

It is believed that the SAT scores for students entering two state universities may have different standard deviations.Specifically,it is believed that the standard deviation at University A is greater than the standard deviation at University B.If a statistical test is to be conducted,which of the following would be the proper way to formulate the null hypothesis?

A small business owner has two fast food restaurants.The owner wants to determine if there is any difference in the variability of service times at the drive-thru window of each restaurant.A sample of size n = 9 is taken from each restaurant's drive-thru window.To perform a hypothesis test using the 0.05 level of significance the critical value is:

In a two-tailed hypothesis test involving two population variances,if the null hypothesis is true then the F-test statistic should be approximately equal to 1.0.

The manager wants to know whether the variances of the sales at two pizza outlets are equal.A sample of 26 days of sales was taken from one outlet and had a sample standard deviation of 30.A sample of 16 days of sales from another had a sample standard deviation of 20.At the 0.05 level of significance,the conclusion is that

The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used.Specifically,the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length.To test whether this is the case,a sample of each seed is used to grow potatoes to maturity.The following information is given: The on these data,if the hypothesis test is conducted using a 0.05 level of significance,the calculated test statistic is: