Question

Please use minitab to solve this question

The following associates were monitoring the process for

              number of defects.

                                                          Good                   #Bad

                             Al                             232                  434

                             Bob                          590                  1199

                             Chris                      45                    83

Is there any relationship between associates and their classifications of products?

              If so, what could cause the differences?

              What would you do next?

Answer 1

Solution:-

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

H₀: Associates and their classifications of products are independent.
H_a: Associates and their classifications of products are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (3 - 1) * (2 - 1)
D.F = 2
E_r,c = (n_r * n_c) / n


Χ² = 0.8214

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 2 degrees of freedom is more extreme than 0.8214.

We use the Chi-Square Distribution Calculator to find P(Χ² > 0.8214) = 0.663

Interpret results. Since the P-value (0.663) is greater than the significance level (0.05), we cannot reject the null hypothesis. Thus, we conclude that there is no  relationship between associates and their classifications of products.

These differences are caused by chance.