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(Sections 6.2, 6.3): Significance testing on the mean when sigma is known

(Section 7.1): Significance testing on the mean with sigma is unknown

book:the practice of statistics for business and economics third edition

Solution

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(Sections 6.2, 6.3): Significance testing on the mean when sigma is known

Z test

Question for single sample z test

An airline wants to evaluate the depth perception of its pilots over the age of fifty. A random sample of n = 14 airline pilots over the age of fifty are asked to judge the distance between two markers placed 20 feet apart at the opposite end of the laboratory. The population standard deviation is 1.4. The sample data listed here are the pilots’ error (recorded in feet) in judging the distance.

2.9 2.6 2.9 2.6 2.4 1.3 2.3 2.2 2.5 2.3 2.8 2.5 2.7 2.6

Is there evidence that the mean error in depth perception for the company’s pilots over the age of fifty is greater than 2.1? Use = 0.05.

(Section 7.1): Significance testing on the mean with sigma is unknown

Single sample t test

Question for single sample t test

As quality control manager at a raisin manufacturing and packaging plant, you want to ensure
that all the boxes of raisins you sell are comparable, with 30 raisins in each box. In the plant,
raisins are poured into boxes until the box reaches its sale weight. To determine whether a
similar number of raisins are poured into each box, you randomly sample 36 boxes about to
leave the plant and count the number of raisins in each. You find the mean number of raisins
in each box to be 29.86, with s = 3.87. Use = 0.01.