1. A manufacturer of batteries claims that the average life of this product will exceed 40 hours. A company is willing to buy a very large shipment if the claim is true. A random sample of 36 batteries is tested and it is found that the sample mean is 45 hours. If the population of batteries has a standard deviation of 5 hours, is it likely that the batteries will be bought?
2. Each student at a university completed a questionnaire concerning the use of advising services. For the entire student body, the mean number of visits per year to an advisor was 3.1. It is hypothesized that this would decrease with the introduction of a student advising service. At the end of the next school year, a random sample of thirty-six students was chosen, for which the mean number of visits was 2.9, with an estimated standard deviation of 1.0. Is this strong evidence that the mean number of visits has decreased? Show all steps of the appropriate test of the hypothesis leading to the conclusion. Use significance level α = 0.10.
3. All freshmen in a particular school were found to have variability in grades expressed as standard deviation of 3. Two samples from among these freshmen, made up of 20 and 50 students each, were found to have means of 88 and 85, respectively. Based on their grades, is the first group really brighter than the second group at alpha = 0.01?
4. A company which sells biscuits claims, "Contents 880 grams", on the package. A sample of 28 packages yields an average of 800 grams. From past experience, the population standard deviation has been 50 grams. Using 0.05 significance level, what conclusions would be drawn concerning the standard which the company is trying to achieve?
5. A certain brand of powdered milk is advertised as having a net weight of 250 grams. If...