Given a sample standard deviation of 6.4 from a sample of 15 observations, construct a 90 percent confi dence interval for the population variance.
MacroSwift has designed a new operating system that will revolutionize the computing industry. The only problem is, the company expects the average amount of time required to learn the software to be 124 hours. Even though this is a long educational time, the company is truly concerned with the variance of the learning time. Preliminary data indicate the variance is 171 hours squared. Recent testing of 25 people found an average learning time of 123 hours and a sample variance of 196.5 hours squared. Do these data indicate the variability in learning time is different from the previous estimate? Test your hypotheses at the 0.02 significance level.
MacroSwift has designed a new operating system that will revolutionize the computing industry. The only problem is, the company expects the average amount of time required to learn the software to be 124 hours. Even though this is a long educational time, the company is truly concerned with the variance of the learning time. Preliminary data indicate the variance is 171 hours squared. Recent testing of 25 people found an average learning time of 123 hours and a sample variance of 196.5 hours squared. Do these data indicate the variability in learning time is different from the previous estimate? Test your hypotheses at the 0.02 significance level.
A psychologist is aware of studies showing that the variability of attention spans of 5-year olds can be summarized by σ 2 = 64 minutes squared. She wonders whether the attention span of 6-year-olds is different. A sample of twenty 6-year-olds gives s2 = 28 minutes squared.
- State explicit null and alternative hypotheses.
- Test your hypotheses at the α = 0.05 level.
- State an explicit conclusion.
In checking its cars for adherence to emissions standards set by the government, an automaker measured emissions of 30 cars. The average number of particles of pollutants emitted was found to be within the required levels, but the sample variance was 50. Find a 90 percent confi dence interval for the variance in emission particles for these cars.
A bank is considering ways to reduce the costs associated with passbook savings accounts. The bank has found that the variance in the number of days between account transactions for passbook accounts is 80 days squared. The bank wants to reduce the variance by discouraging the present use of accounts for short-term storage of cash. Therefore, after implementing a new policy that penalizes the customer with a service charge for withdrawals more than once a month, the bank decides to test for a change in the variance of days between account transactions. From a sample of 25 savings accounts, the bank fi nds the variance between transactions to be 28 days squared. Is the bank justifi ed in claiming that the new policy reduces the variance of days between transactions? Test the hypotheses at the 0.05 level of signifi cance
Sam Bogart, the owner of the Play-It-Again Stereo Company, offers 1-year warranties on all the stereos his company sells. For the 30 stereos that were serviced under the warranty last year, the average cost to fi x a stereo was $75 and sample standard deviation was $15. Calculate a 95 percent confi dence interval for the true standard deviation of the cost of repair. Sam has decided that unless the true standard deviation is less than $20, he will buy his stereos from a different wholesaler. Help Sam test the appropriate hypotheses, using a signifi cance level of 0.01. Should he switch wholesalers?
For two populations thought to have the same variance, the following information was found. A sample of 16 from population 1 exhibited a sample variance of 3.75, and a sample of 10 from population 2 had a variance of 5.38. (a) Calculate the F ratio for the test of equality of variances. (b) Find the critical F value for the upper tail, using the 0.10 signifi cance level. (c) Find the corresponding F value for the lower tail. (d) State the conclusion of your test.
In our study of comparisons between the means of two groups, it was noted that the most common form of the two-group t-test for the difference between two means assumes that the population variances for the two groups are the same. One experimenter, using a control condition and an experimental condition in his study of drug reaction, wished to verify that this assumption held, that is, that the treatment administered affected only the mean, not the variance of the variable under study. From his data, he calculated the variance of the experimental group to be 25.8 and that of the control group to be 20.6. The experimental group had 25 subjects, and the control group had 31. Can he proceed to use the t-test, which assumes equal variances for the two groups? Use α = 0.10.
From a sample of 25 observations, the estimate of the standard deviation of the population was found to be 15.0. From another sample of 14 observations, the estimate was found to be 9.7. Can we accept the hypothesis that the two samples come from populations with equal variances, or must we conclude that the variance of the second population is smaller? Use the 0.01 level of signifi cance.
Minhajur Rahaman
