The maker of a shampoo knows that customers like this product to have a lot of foam. Six sample bottles of the product are selected at random and a procedure is used to produce foam. The foam heights observed are as follows (in millimeters) : 210, 215, 194, 193, 201, 204. (a) Given an estimate for the population mean foam heights and the population variance of the foam heights. For each estimate, base it on an unbiased estimator. (b) Assume that the population is normally distributed. Give a 95% confidence interval for the population variance of the foam heights. (c) Assume that the population is normally distributed. Find a 95% lower confidence bound for the mean foam heights. (d) The maker of the shampoo claims that mean foam heights are more than 195 mm. Based on the lower bound from (c), do the data support the maker's claim ?