The left outside panel of an apartment-size, frost-free refrigerator is designed to have width 235 8 inches. Each hour, 10 such panels are randomly selected from the assembly line and carefully measured. If there is any evidence that the mean width is different from 235 8 inches, the assembly line is shut down for cleaning and inspection. Suppose the distribution of panel widths is normal and s = 0.15.
a. During a specific hour of operation, x 5 23.7 inches. Should the assembly line be shut down? Use a 5 0.05.
b. Using a = 0.05, find the critical values in the x world. (Note: There are two critical values, because this is a two-sided hypothesis test.)
A manufacturer claims the weight of a package of their unsalted pretzels is (at least) 15.5 ounces. To test this claim, a consumer group randomly selected 250 packages and carefully weighed the contents of each. The sample mean was x = 15.45 ounces.
a. Conduct a one-sided, left-tailed hypothesis test to see whether there is any evidence that the true mean weight of the pretzel packages is less than 15.5 ounces. Use a = 0.01 and assume s = 0.26.
b. If your conclusion in part (a) is to reject the null hypothesis, explain how this conclusion is possible even though the sample mean, 15.45, is so close to the hypothesized mean, 15.5. If your conclusion in part (a) is to not reject H0, check those calculations one more time