Chapter 8.1, Problem 4E

Let X equal the thickness of spearmint gum manufactured for vending machines. Assume that the distribution of X is $N\left(\mu ,{\sigma }^2\right)$.

The target thickness is 7.5 hundredths of an inch. We shall test the null hypothesis $H_0:\mu =7.5$ against a two-sided alternative hypothesis, using ten observations.

(a) Define the test statistic and critical region for an $\alpha =0.05$ significance level. Sketch a figure illustrating this critical region.

(b) Calculate the value of the test statistic and state your decision clearly, using the following ii = 10 thicknesses in hundredths of an inch for pieces of gum that were selected randomly from the production line:

7.65 7.60 7.65 7.70 7.55

7.55 7.40 7.40 7.50 7.50

(c) Is $\mu =7.50$ contained in a 95% confidence interval for $\mu$?