Exam 11: Hypothesis Tests and Estimation for Population Variances

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 for the difference between two population variances,the test statistic is an F-ratio formed by putting the larger sample variance in numerator.

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.To test this using an alpha = 0.05 level,a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected.The following sample results were observed: Based on this information,what is the value of the test statistic?

A potato chip manufacturer has two packaging lines and wants to determine if the variances differ between the two lines.They take a sample of n= 15 bags from each line and find the following: The value of the test statistic is F = 1.5

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:

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?

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.

One of the major automobile makers has developed two new engines.At question is whether the two engines have the same variability with respect to miles per gallon.To test this using a significance level equal to 0.10,the following information is available: Based on this situation and the information provided,the critical value is F = 4.147 .

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.

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 .

A machine that is used to fill soda pop cans with pop has an adjustable mean fill setting,but the standard deviation is not supposed to exceed 0.18 ounces.To make sure that this is the case,the managers at the beverage company each day select a random sample of n = 6 cans and measure the fill volume carefully.In one such case,the following data (ounces per can)were observed. Based on these sample data,the test statistic is approximately χ² = 5.01.

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.

In performing a one-tailed test for the difference between two population variances,which of the following statements is true?

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.To test this using an alpha = 0.05 level,a sample of 14 student SAT scores from University A was selected and a sample of 8 SAT scores from University B was selected.The following sample results were observed: Based on this information,what is the critical value that will be used to test the hypothesis?

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: Supplier 1 Supplier 2 n₁ = 9 n₂ = 12 ₁ = 67.25 min ₂ = 72.4 min _s1 = 11.2 min s₂ = 9.9 min Based on these sample results,can the PC maker conclude that a difference exists between the two batteries with respect to the population standard deviations? Test using a 0.10 level of significance.

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,the test statistic for testing whether the two populations have equal variances is F = 1.3733.

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:

A frozen food company that makes burritos currently has employees making burritos by hand.It is considering purchasing equipment to automate the process and wants to determine if the automated process would result in lower variability of burrito weights.It takes a random sample from each process as shown below. In conducting the hypothesis test,the test statistic is F = 1.375.

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 correct null hypothesis for testing whether the variability of the new seed is less than the old seed is:

If the variance of the contents of cans of orange juice is significantly more than 0.003,the manager has to order to stop the filling machine.A sample of 26 cans of orange juice showed a standard deviation of 0.06 ounce.Based on the sample and at the 0.05 level of significance,the filling machine should be