stats problems with solution fall 2014

| August 14, 2017

1. The following are the overall miles per gallon (MPG) of a sample of 2009 sedans priced under $20,000. (27,31,30,28,27,24,29,32,32,27,26,26,25,26,25,24). Construct a 95% confidence interval for the population mean, assuming a normal distribution?2. An analysis wishes to estimate the mean hourly wage of workers in a particular company within 25cents and with a 95% confidence level. The std. dev. of the wages is estimated as being no larger than $1.00. What is the number of personnel records that should be sampled, at minimum, to satisfy the requirements?3. In a recent year, the mean wait for repairs for Verizon customers was 36 hours. In an effort to improve service, a new repair process was developed. This new process, when used on a sample of 90 repairs, resulted in a sample mean of 33 hours and a sample std. dev. of 10 hours.(a) State the null and alternative hypotheses.(b) Is there evidence that the change was successful in reducing the wait time? (use 0.05 level of significance)4. As used in hypothesis testing, describe the null hypothesis and the alternative hypothesis. Can you statistically prove either one?5. A hospital conducted a study of the waiting times in its emergency room at the main campus and three offsite locations. Studying only cases that did not require immediate attention, random samples of 15 were taken at each location on a particular day. The waiting times (from check-in to clinic visit) were measured with the results stored in ER Waiting.(a) At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations? State your null and alternative hypotheses. (Note: while the small sample size could justify use of the non- parametric Kruskal-Wallis rank test, assume normality and use the ANOVA test.(b) Use the Tukey-Kramer procedure tom see which ones are different.6. As reported in the KC Star on July 19, 2013, from a survey commissioned by of 500 motorists, 34% of women cited their husbands as being the worst backseat drivers, while 40% of the men said the same thing about their wives. Assuming 250 of each sex, can we conclude that there is a significant difference in the proportions at a 0.05 level of significance?7. Is there evidence of a significant difference among the various age groups with respect to their major shopping day? Use ? = 0.05. The sample data is summarized in percentages for easy display

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