Sampling distribution

Question

A consulting firm was tasked to design a system to be used to control a clients’ manufacturing processes. The design specification indicates the mean for the process should be 120 and corrective action must be taken whenever the process was not operating satisfactorily in order to eliminate the problem. Suppose the following sample data was collected and provided to the consulting firm.

115 116 119 120 121 120 122 119 123 117 116 120 113 118 120 115

REQUIRED:

Conduct a hypothesis test at the 0.05 level of significance and determine what action, if any, should be taken.

Answer 1

We conduct a two-tailed t-test of hypotheses H₀: µ = 120 H₁: µ =/= 120.

The sample mean was 118.375 and the sample standard deviation was 2.801785145.

This gives a t statistic of ( 118.375 - 120 ) / 2.801785145 / sqrt(16) or t = -2.319949483

Asking Google sheets for the probability we get this value or something more extreme, i.e. the p-value, we get p-value = t.dist.2t(abs(-2.319949483), 15) = 0.03485256763, less than 0.05, and so we reject H₀, and conclude corrective measures need to be taken.

Hope this helps! Let me know if I can explain another method if needed. I can do TI-83/84 as well if preferred.