Exam 11: Hypothesis Tests and Estimation for Population Variances

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: s₁ = 0.09 ounces s₂ = 0.06 ounces The value of the test statistic is F = 1.5

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 0.10 level of significance,the following information is available: Based on this situation and the information provided,the null hypothesis cannot be rejected and it is possible that the two engines produce the same variation in mpg.

In a two-tailed hypothesis test for the difference between two population variances,if s₁ = 3 and s₂ = 5,then the test statistic is F = 1.6667.

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.To conduct a hypothesis test using a 0.05 level of significance,the proper format for the null and alternative hypotheses is (where the current by-hand process is process 1 and the automated process is process 2).

The U.S.Golf Association provides a number of services for its members.One of these is the evaluation of golf equipment to make sure that the equipment satisfies the rules of golf.For example,they regularly test the golf balls made by the various companies that sell balls in the United States.Recently,they undertook a study of two brands of golf balls with the objective to see whether there is a difference in the mean distance that the two golf ball brands will fly off the tee.To conduct the test,the U.S.G.A.uses a robot named "Iron Byron," which swings the club at the same speed and with the same swing pattern each time it is used.The following data reflect sample data for a random sample of balls of each brand. Given this information,what is the test statistic for testing whether the two population variances are equal?

When conducting a one-tailed hypothesis test of a population variance using a sample size of n = 24 and a 0.10 level of significance,the critical value is:

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:

A contract calls for the strength of a steel rod to stand up to pressure of 200 lbs per square inch on average.The contract also requires that the variability in strength for individual steel rods be no more than 5 pounds per square inch.If a random sample of n = 15 rod is selected and the sample standard deviation is 6.7 pounds,the test statistic is approximately χ² = 25.138.

Assume a sample of size n = 12 has been collected.To perform a hypothesis test of a population variance using a 0.05 level of significance,where the null hypothesis is: H_o : σ² = 25. The upper tail critical value is 21.92.

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 correct null and alternative hypotheses would be:

If a hypothesis test for a single population variance is to be conducted,which of the following statements is true?

The F-distribution is used to test whether two sample variances are equal.

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.

A first step in testing whether two populations have the same mean value using the t-distribution is to use the chi-square distribution to test whether the populations have equal variances.

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 standard deviations? Test using a 0.10 level of significance.

A sample of n observations is taken from a normally distributed population to estimate the population variance.The degrees of freedom for the chi-square distribution are n-2.

In a hypothesis test for the equality of two variances,the lower-tail critical value does not need to be found as long as the larger sample variance is placed in the denominator of the test statistic.

Which of the following is the appropriate null hypothesis when testing whether two population variances are equal?

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.

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?