Test for one sample mean
1. A major tire manufacturer wishes to estimate mean tread life in miles for one of their tires. They want to develop the confidence interval estimate that would've the maximum sampling error of 500 miles with 90 percent confidence. A pilot sample of n = 50 tires showed the sample standard deviation equal to 4,000 miles. Based upon this information, the required sample size is:
2. One of the factors that the company will employ in determining whether it will locate the new facility in a community is status of the real estate market. The managers believe that an significant measure of the real estate market is the average length of time that homes stay on market before selling. They believe that if the mean time on market is less than 45 days, the real estate market is favorable. To test this in the particular area, a random sample of n = 100 homes that sold throughout the past six months was selected. The mean for this sample was 40 days. It is believed that population standard deviation is 15 days. If the test is conducted using the 0.05 level of significance, what conclusion should be reached?