1. The administrators of a hospital want to estimate the myer- age number of days required to treat patients before they are released. A random sample of 500 hospital patients has mean 5.4 days and standard deviation Al days. Construct a 92% confidence interval for the average length of stay of patients in this hospital. 2. In 1983, a survey was conducted using a sample of 1251 Americans. Among the people surveyed, 218 declared that they were using their seat belts while driving. Find a 90% confidence interval for the proportion of all Americans wing their seat belts in 1943. 4. Organic chemists often purify organic compounds by a method known as fractional crystallization. An experimenter wants to prepare and purify 4.85g of aniline. Ten specimens of aniline are prepared and purified to produce acctanilide. The wrights (in grams) of the results are: 285, 2.88, 390, 2.62 3.72, 180, 3.85, 3.36, 4.01, 1.42. Assume that the distribution of weights follows a normal dis- tribution. (a) Construct a 90% confidence Interval for the average weight of acctanilide that can be recovered from this pro- (b) Construct a $7% confidence interval for the variance of the weights of the results. 4. Gasoline pumped from a supplier's pipeline is supposed to have an octane rating of 87.5. On a sample of 13 consecutive days, the octane rating was measured; this sample gave an average rating of 87.16 with a standard deviation of 0.7131. (a) Construct a 90% confidence interval for the true average octane rating. (b) Interpret your answer from part (a). (e) Construct a 90% confidence interval for the true standard devintion. (d) What assumption did you make for constructing the con- Aldence intervals in this problem? If you were given the raw data for this sample, how would you check if this assumption is valid