1. A manufacturer claims that the thickness of the spearmint gum it produces is 7.5 one-hundredths of an inch. A quality control specialist regularly checks this claim. On one production run, he took a random sample of pieces of gum and measured their thickness. He obtained:

7.65 7.60 7.62 7.68 7.56 7.58 7.43 7.45 7.51 7.54

1. Use a significance level of 0.05 to test the manufacturer's claim. Show all 6 steps of the hypothesis test.
2. It is also important to make sure that the gum thickness is consistent. The manufacturer would like the standard deviation of gum thicknesses to be less than 0.10 one-hundredths of an inch. Show all 6 steps of a hypothesis test to determine if the manufacturer should be worried about the variability of the thickness of their spearmint gum.
3. What assumptions are made when performing the hypothesis tests in parts a and b?