Question

A manufacturer of t-shirts marks a shirt as "irregular" when it has defects such as crooked seams, stains, rips, or holes. A small number of irregular t-shirts are expected as part of the manufacturing process, but if more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process. In order to test whether his plant is making a higher than expected number of irregular t-shirts, the manager of a plant randomly selects 100 t-shirts and finds that 12 are irregular. He plans to test the hypothesis: H0, P = 0.08, versus Ha, p > 0.08 (where p is the true proportion of irregular t-shirts). What is the test statistic

Answer 1

The test statistic value is 1.474.

Explanation:

In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.

If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..

The hypothesis for this test can be defined as follows:

H₀: The proportion of irregular t-shirts is 8%, i.e. p = 0.08.

Hₐ: The proportion of irregular t-shirts is more than 8%, i.e. p > 0.08.

The information provided is:

n = 100

X = number of irregular t-shirts = 12

Compute the sample proportion as follows:

`\hat p=(X)/(n)=(12)/(100)=0.12`

Compute the test statistic as follows:

`t=\frac{\hat p-p}{\sqrt{(p(1-p))/(n)}}`

`=\frac{0.12-0.08}{\sqrt{(0.08(1-0.08))/(100)}}\\\\=1.47441\\\\\approx 1.474`

Thus, the test statistic value is 1.474.