Probability and Statistical Inference (9th Edition)
Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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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 ( μ , σ 2 ) .

The target thickness is 7.5 hundredths of an inch. We shall test the null hypothesis H 0 : μ = 7.5 against a two-sided alternative hypothesis, using ten 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 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 μ = 7.50 contained in a 95% confidence interval for μ ?

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