1. A bakery wants to determine the average amount of honey used in a certain type of honey cake. An examination of 64 honey cakes revealed that they contained an average of 8.0 ounces of honey, with σ = 0.5 ounce. If 8 ounces of honey is used as an estimate of the actual mean number of ounces per cake, what can we assert about the maximum error
(a) with 95% confidence:
(b) with 99% confidence?
2. Before purchasing a large shipment of ground meat, a sausage manufacturer wants to be 95% confident that he is in error by no more than 2 grams in estimating the fat content (per 100 grams). If the standard deviation of the fat content (per 100 grams) is assumed to be 8 grams, on how large a sample should he based his estimate?
3. A beauty parlor finds that in n = 60 randomly selected days it had, on average, x = 72.3 patron per day with a standard deviation of s = 8.5 patrons.
(a) Construct a 90% confidence interval for the actual daily average number of beauty parlor patrons.
(b) using the data of this exercise, but changing x = 72.3 to x = 82.3, recalculate the 90% confidence interval for the actual daily average number of beauty parlor patrons.
4. In a study of automobile insurance costs, a random sample of n = 70 body repair costs on a particular kind of damage had a mean of x= $529.35 and a standard deviation of s = $66.23. If $529.35 is used as an estimate of the true average cost of such repairs, what can we say about the possible error with a probability of 0.95?