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

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

Describe the rank correlation test. What types of hypotheses is it used to test? How does the rank correlation coefficient rs differ from the Pearson correlation coefficient r?

Use the data in the given table and the corresponding Minitab display to test the hypothesis._ The following table entries are test scores for males and females at different times of day. Assuming no effect from the interaction between gender and test time, test the claim that time of day does not affect test scores. Use a 0.05 significance level. 6 a.m. - a.m. a.m. - p.m. p.m. - p.m. p.m. - p.m. Male 87 89 92 85 Female 72 84 94 89 Source DF SS MS F p Gender 1 24.5 24.5 0.6652 0.4745 Time 3 183 61 1.6561 0.3444 Error 3 110.5 36.83 Total 7 318

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

Use the rank correlation coefficient to test for a correlation between the two variables. Use the sample data below to find the rank correlation coefficient and test the claim of correlation between math and verbal scores. Use a significance level of 0.05. Mathematics 347 440 327 456 427 349 377 398 425 Verbal 285 378 243 371 340 271 294 322 385

Which of the following is NOT a requirement for one-way ANOVA?

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

R charts are used to monitor_____________._

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.

Construct a run chart for individual values corresponding to the given data. 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 Box Weight (Ib) 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

ANOVA requires usage of the _______ distribution.

In a study of the effectiveness of physical exercise in weight reduction, 12 subjects followed a program of physical exercise for two months. Their weights (in pounds)before and after this Program are shown in the table. Use Wilcoxon's signed -ranks test and a significance level of 0.05 to test the claim that the exercise program has no effect on weight. Before 162 190 188 152 148 127 195 164 175 156 180 136 After 157 194 179 149 135 130 183 168 168 148 170 138 What would be the signed rank for the column with values of 175 and 168 ?

Given below are the analysis of variance results from a Minitab display._ to use a 0.05 significance level in testing the null hypothesis that the different samples come From populations with the same mean. Identify the P-value. Source DF SS MS F p Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

Describe a run chart and give an example. Refer to the values on each of the axes as you describe the run chart.

Use the Wilcoxon rank-sum approach to test the claim that the two independent sample student_ grade averages at two colleges come from populations with equal medians. The sample data is listed below. Use a 0.05 level of significance, and assume that the samples were randomly selected. College A 3.2 4.0 2.4 2.6 2.0 1.8 1.3 0.0 0.5 1.4 2.9 College B 2.4 1.9 0.3 0.8 2.8 3.0 3.1 3.1 3.1 3.5 3.5

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

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 32 27 22 34 24 25 37 33 32 33 30 22 36 21 39

Use the data in the given table and the corresponding Minitab display to test the hypothesis. The_ following Minitab display results from a study in which three different teachers taught calculus classes of five different sizes. The class average was recorded for each class. Assuming no effect from the interaction between teacher and class size, test the claim that the teacher has no effect on the class average. Use a 0.05 significance level. Source D Teacher 2 56.93 28.47 1.018 0.404 Class Size 4 672.67 168.17 6.013 0.016 Error 8 223.73 27.97 Total 14 953.33

Control charts are used to monitor changing characteristics of data over ____________._

The data below represent the weight losses for people on three diets. Diet A Diet B Diet C 1.75 3.8 4.8 8.8 4.9 6.2 7.3 1.1 5.8 9.8 7.8 8.1 5.1 1.2 6.9 If we want to test the claim that the three size categories have the same means, why don't we use three separate hypothesis tests for $\mu _ { 1 } = \mu _ { 2 } , \mu _ { 2 } = \mu _ { 3 }$ , and $\mu _ { 1 } = \mu _ { 3 }$ ?