You have concluded the data collection activity for your research. In a prior st

Question

You have concluded the data collection activity for your research. In a prior stage, you identified a research question related to a dilemma your organization faced regarding poor product quality.

The results from your experiment seems to support your thinking that a new process will improve quality. research into the process and product determined a particular part was not dimensionally correct. It needed to be no less than 25mm.

Here is the data from a test run after the change to the process was implemented. Outline the steps in the hypothesis testing procedure you would need to do to substantiate your claim.

n = 30, x-bar = 26.5mm, s = 2.4mm

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 25

Alternative hypothesis: < 25

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.4382

DF = n - 1 = 30 - 1

D.F = 29

t = (x - ) / SE

t = 3.42

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 3.42

Thus the P-value in this analysis is 0.9991

Interpret results. Since the P-value (0.9991) is greater than the significance level (0.01), we have to accept the null hypothesis.

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