Exam 12: Statistical Control Charts, Nonparametric Tests, and Hypothesis Testing

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

At the same time each day, a researcher records the temperature in each of three classrooms. The table shows the temperatures in degrees Fahrenheit recorded for one week. Classroom \#1 Classroom \#2 Classroom \#3 78 71 77 75 69 73 73 72 72 66 72 71 68 65 70 71 73 62 72 71 79 How are the analysis of variance results affected if the same constant is added to every one of The original sample values?

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 $R _ { 1 }$ that would be used in finding $H$ ?

Match the chart with its characteristic. -Each sample belongs to one of two categories (such as defective or not defective).

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

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.

List the assumptions for testing hypotheses that three or more means are equivalent._

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from_ populations with equal medians. SAT scores for students selected randomly from two different schools are shown below. Use a significance level of 0.05 to test the claim that the scores for the two schools are from populations with the same median. School A School B 550 480 670 460 580 620 400 700 520 380 680 570 540 740 560 660 500 480 360 560 650 600 550

Construct an $\bar { x }$ chart. Control Chart Constants s R n 2 1.880 2.659 0.000 3.267 0.000 3.267 3 1.023 1.954 0.000 2.568 0.000 2.574 4 0.729 1.628 0.000 2.266 0.000 2.282 5 0.577 1.427 0.000 2.089 0.000 2.114 6 0.483 1.287 0.030 1.970 0.000 2.004 7 0.419 1.182 0.118 1.882 0.076 1.924 8 0.373 1.099 0.185 1.815 0.136 1.864 9 0.337 1.032 0.239 1.761 0.184 1.816 10 0.308 0.975 0.284 1.716 0.223 1.777 A machine is supposed to fill boxes to a weight of 50 pounds. Every 30 minutes a sample of four boxes is tested; the results are given below. Sample Beight (lb) Range 1 49 38 39 45 42.75 11 2 52 51 43 61 51.75 18 3 56 60 32 52 50.00 28 4 44 59 46 49 49.50 15 5 51 61 48 45 51.25 16 6 45 50 46 48 47.25 5 7 52 51 45 55 50.75 10 8 40 50 53 48 47.75 13 9 48 67 60 51 56.50 19 10 43 50 50 47 47.50 7 11 48 30 38 39 38.75 18 12 50 46 48 53 49.25 7 13 50 58 56 64 57.00 14 14 47 52 47 49 48.75 5 15 52 57 58 52 54.75 6

Construct an R chart and determine whether the process variation is within statistical control. Control Chart Constants $\text { Control Chart Constants }$ s R n 2 1.880 2.659 0.000 3.267 0.000 3.267 3 1.023 1.954 0.000 2.568 0.000 2.574 4 0.729 1.628 0.000 2.266 0.000 2.282 5 0.577 1.427 0.000 2.089 0.000 2.114 6 0.483 1.287 0.030 1.970 0.000 2.004 7 0.419 1.182 0.118 1.882 0.076 1.924 8 0.373 1.099 0.185 1.815 0.136 1.864 9 0.337 1.032 0.239 1.761 0.184 1.816 10 0.308 0.975 0.284 1.716 0.223 1.777 A machine is supposed to fill cans that contain 12 ounces. Each hour, a sample of four cans is tested; the results of 15 consecutive hours are given below. Sample Can Volume (oz) Range 1 11.2 11.7 11.8 11.7 11.600 0.6 2 11.8 11.3 11.6 11.6 11.575 0.5 3 11.3 12.0 11.8 11.7 11.700 0.7 4 12.1 11.6 12.1 12.0 11.950 0.5 5 11.8 11.8 11.9 11.9 11.850 0.1 6 12.0 11.9 11.8 11.7 11.850 0.3 7 11.6 12.0 11.9 11.8 11.825 0.4 8 11.5 12.1 11.9 12.0 11.875 0.6 9 12.1 12.1 11.7 11.9 11.950 0.4 10 11.7 12.0 11.6 11.9 11.800 0.4 11 12.1 12.4 11.9 12.2 12.150 0.5 12 12.5 12.0 12.4 12.3 12.300 0.5 13 12.5 12.0 12.1 12.1 12.175 0.5 14 12.4 12.0 12.0 12.4 12.200 0.4 15 12.4 12.4 12.6 12.1 12.375 0.5

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

The following data contains task completion times, in minutes, categorized according to the_ gender of the machine operator and the machine used. Male Female Machine 1 15,17 16,17 Machine 2 14,13 15,13 Machine 3 16,18 17,19 Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results affected if 5 minutes is added to each completion time?

There is a(n)____________________ between two factors if the effect of one of the factors changes for different categories of the other factor.

Match the nonparametric test with its related parametric test._ Runs test

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.

The following data shows annual income, in thousands of dollars, categorized according to the_ two factors of gender and level of education. Assume that incomes are not affected by an interaction between gender and level of education, and test the null hypothesis that level of education has no effect on income. Use a 0.05 significance level. Female Male High school 23,27,24,26 25,26,22,24 College 28,36,31,33 35,32,39,28 Advanced degree 41,38,43,49 35,50,47,44

A machine that is supposed to fill small bottles to contain 20 milliliters yields the following data from a test of 4 bottles every hour. What would be the centerline for a control chart for $\bar{x} ?$ Sample bottle Volume (oz) Range 1 19.9 20.1 20.2 20.3 20.125 0.4 2 20.4 20.0 20.3 20.3 20.250 0.4 3 20.0 20.7 20.4 20.3 20.350 0.7 4 20.4 20.1 20.1 19.9 20.125 0.5 5 19.9 19.8 19.6 19.5 19.700 0.4 6 19.4 19.4 19.6 19.7 19.525 0.3 7 19.8 19.4 19.6 19.7 19.625 0.4 8 19.9 19.8 20.0 20.0 19.925 0.2 9 20.2 20.3 20.1 20.3 20.225 0.2 10 20.0 20.3 20.0 20.2 20.125 0.3 11 20.3 20.5 20.1 20.2 20.275 0.4 12 20.1 19.9 19.8 19.7 19.875 0.4 13 19.5 19.8 19.7 19.6 19.650 0.3 14 19.4 19.8 19.8 19.4 19.400 0.4 15 19.5 19.6 19.6 19.9 19.650 0.4

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

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

Describe the sign test. What types of hypotheses is it used to test? What is the underlying_ concept?