Exam 11: Hypothesis Tests and Estimation for Population Variances

Which of the following is the appropriate null hypothesis when testing whether two population 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. To conduct a hypothesis test using a 0.05 level of significance,the critical value is 3.347.

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?

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.

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.

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,the following information is available: Based on this situation and the information provided,the test statistic is 1.2118.

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.

A fast food restaurant that sells burritos is concerned about the variability in the amount of filling that different employees place in the burritos.To achieve product consistency it needs this variability to be no more than 1.7 ounces.A sample of n = 18 burritos showed a sample variance of 2.89 ounces.Using a 0.10 level of significance,what can you conclude?

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.

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 null hypothesis should be rejected since the test statistic exceeds the F-critical value from the F-distribution table.

Which distribution is used in testing the hypotheses about the equality of two population variances?

There are two major companies that provide SAT test tutoring for high school students.At issue is whether Company 1,which has been in business for the longer time,provides better results than Company 2,the newer company.Specifically of interest is whether the mean increase in SAT scores for students who have already taken the SAT test one time is higher for Company 1 than for Company 2.Two random samples of students are selected.The following data reflect the number of points higher (or lower)that the students scored on the SAT test after taking the tutoring.Prior to conducting the test,which compares the means,we should determine if the assumption of equal variances is supported. Conduct the appropriate hypothesis test to determine if the assumption of equal variances is supported using a 0.10 level of significance.

In a two-tailed test for the equality of two variances,the critical value is determined by going to the F-distribution table with an upper-tail area equal to alpha divided by two.

Because of the way the F-distribution is formed,all F-tests are one-tailed tests.

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.

A potato chip manufacturer has found that in the past the standard deviation of bag weight has been 0.2 ounce.They want to test whether the standard deviation has changed.The null hypothesis is:

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 inch.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 inch.Testing at the 0.05 level of significance,which of the following is true?

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?

In a test for determining whether two population variances are the same or different,the larger the sample sizes from the two populations,the lower will be the chance of making a Type I statistical error.