MAT 2058 Test #3 (covers Chapters 7 and 8) Open book, open notes - 10 points total Name: ________________________________ 1) (5 points) Regarding your final project, provide the confidence intervals for the mean costs for the six items you have selected. Perform the hypothesis test for the project to determine if the mean costs for the 6 items at each of the 3 stores are the same ( = 0.05). Use the ANOVA: Single Factor analysis in Excel, as was described in Week 8, to determine whether to reject or fail to reject the null hypothesis, that the mean costs at the three grocery stores are the same. Make sure that you submit a copy of this with your Test #3. 2) (0.5 points) Of 265 randomly selected medical students, 83 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community. ____________________< p < ____________________ 3) (0.5 points) Use a confidence level of 95% to estimate the population mean for test scores, given a sample set of test scores with a sample size of 150, sample mean of 75.5, and standard deviation of 5.2. Round your answer to the same number of decimal places as the sample mean. ____________________< < ____________________ 4) (0.5 points) Assume that a sample is used to estimate a population mean. Us a confidence level of 95%, a sample size of 45, sample mean of 5.4, and sample standard deviation of 0.93 to find the margin of error. Assume that the sample is a simple random sample and the population has a normal distribution. Round your answer to one more decimal place that the sample standard deviation. E = ______________________ Page 1 of 2 5) (0.5 points) To find the standard deviation of the diameter of wooden dowels, the manufacturer measure 19 randomly selected dowels and find the standard deviation of the sample to be s = 0.16. Find the 95% confidence interval for the population standard deviation. Assume that the population has a normal distribution. Round the confidence interval limits to the same number of decimal places as the sample standard deviation. ________________ < < ________________ 6) (3 points; 0.5 points per answer) In tests of a computer component, the mean time between failures has been 519 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures: 518 548 561 523 536 499 538 557 528 563 Based on these data, the sample mean is calculated to be 537.1 hours and the sample standard deviation is 20.7 hours. At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 519 hours. Use the critical value method of testing hypotheses. a) H0: _____________________________________________ b) H1: _____________________________________________ c) Test statistic: _____________________________________ d) Critical value: ____________________________________ e) Do you reject H0? _____________________ f) If you were told that the p-value for the test statistic for this hypothesis test is 0.014, would you reach the same decision that you made in (e) and (f)? Yes No Page 2 of 2