PROBLEM 4E

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 an 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?

practice dhawan.chaitanya January 2017 1 Introduction This is a practice submission. These are no notes. There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened. 2 Conclusion \I always thought something was fundamentally wrong with the universe" () 1