Exam 12: Control Charts and Process Monitoring

Use the runs test to determine whether the given sequence is random. Use a significance level of 0.05. The sequence of numbers below represents the maximum temperature (in degrees Fahrenheit)in July in one U.S. town for 30 consecutive years. Test the sequence for randomness above and below the median. 94 96 97 99 95 90 97 98 100 100 92 95 98 99 102 97 97 101 99 100 98 95 93 99 101 99 101 100 99 103

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05. Brand A Brand B Brand C n=10 n=10 n=10 =32.1 =32.6 =27.2 =4.37 =3.61 =3.34

Describe the Wilcoxon rank-sum test. What type of hypotheses is it used to test? What assumptions are made for this test? What is the underlying concept?

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 three brands have the same mean if the following sample results have been obtained. Brand A Brand B Brand C 32 27 22 34 24 25 37 33 32 33 30 22 36 21 39

Use the runs test to determine whether the given sequence is random. Use a significance level of 0.05. The sequence of numbers below represents the maximum temperature (in degrees Fahrenheit)in July in one U.S. town for 30 consecutive years. Test the sequence for randomness above and below the median. 94 96 97 99 95 90 97 98 100 100 92 95 98 99 102 97 97 101 99 100 98 95 93 99 101 99 101 100 99 103

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 The ANOVA results lead us to conclude that the completion times are not affected by an interaction between machine and gender, and the times are not affected by gender, but they are affected by the machine. Change the table entries so that there is an effect from the interaction between machine and gender.

Use the sign test to test the indicated claim. A researcher wishes to test whether a particular diet has an effect on blood pressure. The blood pressure of 24 randomly selected adults is Measured. After one month on the diet, each person's blood pressure is again measured. For 18 people, the second blood pressure reading was lower than the first, and for 6 people, the Second blood pressure reading was higher than the first. At the 0.01 significance level, test the Claim that the diet has an effect on blood pressure. What would be the value of the test Statistic, x?

Give at least two examples of nonparametric tests and their comparable parametric tests.

The centerline for a control chart for R consists of _______________.

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 rejectio of a statistically stable mean.

R charts are used to monitor_____________.

Use the sign test to test the indicated claim. A researcher wishes to test whether a particular diet has an effect on blood pressure. The blood pressure of 25 randomly selected adults is measured. After one month on the diet, each person's blood pressure is again measured. For 19 people, the second blood pressure reading was lower than the first, and for 6 people, the second blood pressure reading was higher than the first. At the 0.01 significance level, test the claim that the diet has an effect on blood pressure.

ANOVA requires usage of the _______ distribution.

Why do researchers concentrate on explaining an interaction in a two-way ANOVA rather than the effects of each factor separately?

Examine the given run chart or control chart and determine whether the process is within statistical control. If it is not, identify which of the three out-of-statistical-control criteria apply.

Solve the problem. Critical values for the runs test for randomness can be calculated by listing all possible sequences. Using the elements B, B, B, R, R, R list the 20 different possible sequences. Find the number of runs for each sequence. Are you able to find 5% cutoff values for G? What do you conclude?

Provide an appropriate response. A common goal of quality control is to reduce variation in a product or service. List and describe the two types of variability. Give an example of each.

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

Use a Kruskal-Wallis test to test the claim that the samples come from populations with equal medians. The table below shows the weights (in pounds)of 6 randomly selected women in each of three different age groups. Use a 0.01 significance level to test the claim that the 3 age-groups have the same median weight. 18-34 35-55 56 and older 119 123 140 134 147 128 114 135 59 125 110 134 153 154 120 138 163 116

______________? measurement of a characteristic or good or services that result from some combination of Equipment, people, materials, methods, and conditions.