# Question

Let X equal the thickness of spearmint gum manufactured for vending machines. Assume that the distribution of X is N(μ, σ2). The target thickness is 7.5 hundredths of a n inch. We shall test the null hypothesis H0: μ = 7.5 against a two-sided alternative hypothesis, using 10 observations.
(a) Define the test statistic and critical region for an α = 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 n = 10 thicknesses in hundredths of an inch for pieces of gum that were selected randomly from the production line:
(c) Is μ = 7.50 contained in a 95% confidence interval for μ?

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• CreatedOctober 12, 2015
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