A machine has been designed to make nails which are 8cm long with a standard deviation of 0.15cm. A sample of 48 nails is selected periodically to assess if the length is too variable from the standard of 8cm. From the sample of 48 nails, the mean is found to be 7.983cm. Assume the lengths are normally distributed.
-The test statistic is _____.
A)-0.785
B)-1.57
C)-3.04
D)1.57
E)0.785

Question

Quizplus · Accepted Answer

The test statistic is calculated as (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. In this case, x̄ = 7.983cm, μ = 8cm, σ = 0.15cm, and n = 48. Plugging these values into the formula, we get (7.983 - 8) / (0.15 / √48) = -0.785.

A Machine Has Been Designed to Make Nails Which Are