This is the Sample Size Determination & Hypothesis Testing Example 1 Problem Set for OMGT6123.  Please peruse the video tutorial of the solution posted to the course website. 

OMGT6123 Sample Size Determination & Hypothesis Testing Example Set

1.  Jennifer intends to estimate the average driving time of a large group of commuters (n>30). From a previous study, she believes that the average time is 42 minutes with a sample standard deviation of 9 minutes. She wants a two tailed 95 percent confidence interval with a sampling error of 3 minutes.

          a.     Help Jennifer find the the smallest sample size that she should consider?

          b.     Someone said that if the variance of the data doubled that the sample size would double.  Is this true?  Show your work and process.

2.  A 95% confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following confidence interval: (0.438, 0.642).

a.    Using the given information, what is the sampling error for the problem & what is the standard deviation of the sample?

b.    Again, using the given & calculated information, what sample size would be necessary if we wanted to estimate the true proportion with the same sampling error but now with 99% confidence?

3.  A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the weight of the chicken.  The store advertises that the average weight of their chicken is 4.6 pounds (population mean). A random sample of 30 of the store's chickens yielded the weights (in pounds) shown below.

Test whether the mean weight of the chickens is equal to 4.6 pounds. Use a 95% confidence level.  Explain what this result means in business terms for the supermarket.

4.  Jimmy's Junk Warehouses use thousands of fluorescent light bulbs each year. The brand of bulb it currently uses has a mean life of 700 hours. A competitor claims that its bulbs, which cost the same as the brand Jimmy's Warehouses currently use, have a mean life different than 700 hours. Jimmy's purchasing manager has decided to purchase the new brand if, when tested, the evidence supports the manufacturer's claim at the 0.05 significance level. Suppose 36 bulbs were tested with the following results: xbar=720 hours, s=60 hours. Conduct a two tailed test using a confidence level of 95% & explain what the results are telling Jimmy's purchasing manager (i.e., is the bulb life of the new bulbs any different than the original bulb life).

5.  A large university is interested in learning about the average time it takes students to drive to  campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a hypothesis test.  The goal was to determine if the average travel time of all the university 's students differed from the stated 20 minutes in the university's brochure. Suppose the sample mean and sample standard deviation were calculated to be 23.2 and 20.26 minutes, respectively.

a.  Calculate the value of the test statistic to be used in the test.

b.  At the 99% confidence level, does the university's claim of 20 minutes student commute time is realistic/accurate?