Exam 12: Control Charts and Process Monitoring

Find the critical value. Assume that the test is two -tailed and that $n$ denotes the number of pairs of data. $n = 20 , \alpha = 0.01$

Use the sign test to test the indicated claim. Fourteen people rated two brands of soda on a scale of 1 to 5. Brand A 2 3 2 4 3 1 2 Brand B 1 4 5 5 1 2 3 Brand A 5 4 2 1 1 4 3 Brand B 4 5 5 2 4 5 4 At the 5 percent level, test the null hypothesis that the two brands of soda are equally popular.

Which statement is false about the Wilcoxon signed-ranks test?

Construct a run chart for individual values corresponding to the given data. A machine that is supposed to produce ball bearings with a diameter of 7 millimeters yields the following data from a test of 5 ball bearings every 20 minutes. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Ball Bearing Diameter }(\mathrm{mm} \text { ) }$ Sample Range 1 6.3 6.8 6.9 6.8 6.9 6.74 0.6 2 6.3 6.6 6.6 6.3 7.0 6.56 0.7 3 6.8 6.7 7.0 6.5 7.0 6.80 0.5 4 7.0 6.7 6.7 6.8 6.8 6.80 0.3 5 6.8 6.8 6.6 6.5 6.4 6.62 0.4 6 6.8 6.7 6.6 6.3 6.9 6.66 0.6 7 7.3 7.3 7.4 7.4 7.0 7.28 0.4 8 7.2 7.0 7.2 6.9 7.1 7.08 0.3 9 7.3 7.6 7.1 7.4 7.6 7.40 0.5 10 7.2 7.6 7.5 7.6 7.1 7.40 0.5 11 7.2 7.2 7.4 7.0 7.0 7.16 0.4 12 7.5 7.4 7.4 7.6 7.1 7.40 0.5

A control chart for $\bar { x }$ is shown below. Determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of a statistically stable mean.

Suppose you are to test for equality of four different population means, with $H _ { 0 } : \mu _ { A } = \mu _ { B } = \mu _ { C } = \mu _ { D }$ . Write the hypotheses for the paired tests. Use methods of probability to explain why the process of ANOVA has a higher degree of confidence than testing each of the pairs separately.

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. At the $0.025$ significance level, test the claim that the four brands have the same mean if the following sample results have been obtained. Brand A Brand B Brand C Brand D 17 18 21 22 20 18 24 25 21 23 25 27 22 25 26 29 21 26 29 35 29 36 37

Use the sign test to test the indicated claim. The waiting times (in minutes)of 28 randomly selected customers in a bank are given below. Use a significance level of 0.05 to test the claim that the population median is equal to 5.3 minutes. 8.2 8.0 10.5 3.8 6.4 5.3 7.8 2.9 6.0 7.7 6.1 5.9 1.2 10.4 7.3 6.9 5.8 5.1 6.2 3.1 5.8 11.7 4.5 6.5 9.8 7.4 2.3 7.8

Which of the following is not one of the criteria for determining if a control chart indicates that a process is not statistically stable?

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

Use a Kruskal-Wallis test to test the claim that the samples come from populations with equal medians. Listed below are grade averages for randomly selected students with three different categories of high-school background. At the 0.05 level of significance, test the claim that the three groups have the same median grade average. HIGH SCHOOL RECORD Good Fair Poor 3.21 2.87 2.01 3.65 3.05 2.31 1.00 2.00 2.98 3.12 0.00 0.50 2.75 1.98 2.36

A _________________ is a sequential plot of individual data values over time. One axis is used for the data values, and the other axis is used for the time sequence.

Define statistically stable (or "within statistical control"). Show examples of run charts which illustrate processes which are not statistically controlled. Discuss the pattern which indicates the process is not statistically controlled for each example.

Why is it unnecessary to conduct multiple comparison tests after a nonsignificant F test statistic results?

Four different judges each rank the quality of 20 different singers. What method can be used for agreement among the four judges?

Use a Kruskal-Wallis test to test the claim that the samples come from populations with equal medians. SAT scores for students selected randomly from three different schools are shown Below. Use a significance level of 0.05 to test the claim that the students from the three Schools had the same median SAT score. School 1 School 2 School 3 550 480 670 460 580 620 500 620 700 400 600 520 380 600 470 450 550 760 What would be the value of R1 that would be used in finding H?

Use the Wilcoxon signed -ranks test to test the claim that the matched pairs have differences that come from a population with a median equal to zero. Eleven runners are timed at the 100- meter dash and are timed again one month later after following a new training program. The times (in seconds)are shown in the table. Use Wilcoxon's signed-ranks test and a significance level of 0.05 to test the claim that the training has no effect on the times. Before 12.1 12.4 11.7 11.5 11.0 11.8 12.3 10.8 12.6 12.7 10.7 After 11.9 12.4 11.8 11.4 11.2 11.5 12.0 10.9 12.0 12.2 11.1

Explain the procedure for two-way analysis of variance, and how it varies depending on whether there is an interaction between the two factors or not.

Use the given process data to construct a control chart for p. A drugstore considers a wait of more than 5 minutes to be a defect. Each week 100 customers are randomly selected and timed at the checkout line. The numbers of defects for 20 consecutive weeks are given below. 4 4 5 5 5 5 5 6 6 6 6 12 6 6 6 7 6 7 8 7