The Journal de Botanique reported that the mean height of Begonias grown while being treated with a particular nutrient is 33 centimeters. To check whether this is still accurate, heights are measured for a random sample of 17 Begonias grown while being treated with the nutrient. The sample mean and the sample standard deviation of those height measurements are 38 centimeters and 8 centimeters, respectively. Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample, can it be concluded that the population mean height of treated Begonias, u, is different from that reported in the journal? Use the 0.05 level of significance. Perform a two-tailed test. Carry your intermediate computations to 3 or more decimal places.
a) State the null and alternative hypothesis.
b) Determine the type of test statistic to use.
c) Find the value of the test statistic. Round to 3 or more decimal places. d) Find the p-value. Round to 3 or more decimal places.