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

A control chart for R is shown below. Determine whether the process variation is within_ statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation.

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 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?

The test statistic for one-way ANOVA is equal to _________________. A) $\frac { \text { Variance within samples } } { \text { Variance between samples } }$ B) $\frac { \text { Variance between samples } } { \text { Variance within samples } }$ C) $\frac { \text { Mean within samples } } { \text { Mean between samples } }$ D) $\frac { \text { Variance within populations } } { \text { Variance between populations } }$

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.

Match the parametric test with its comparable nonparametric test. 1)matched pair t test 2)two independent samples t test 3)analysis of variance (F test) 4)linear correlation A)rank correlation test B)Wilcoxon rank-sum test C)Kruskal-Wallis test D)sign test

Use the runs test to determine whether the given sequence is random. Use a significance level_ of 0.05. Test the sequence of digits below for randomness above and below the value of 4.5. 0 4 7 3 6 0 9 7 4 8 7 2 8 5 7 3 9 6 4 6 4 7 9 1 6 1 9 5 8 3 7 8 5 7 3 5 2 9 3 8

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.

Match the chart with its characteristic. -Monitors variation in a process

A control chart for attributes is to be constructed. limits, a process which has been having a 5% rate of nonconforming items, or a process which has been having a 10% of nonconforming items? Assume that both processes have the same sample sizes. For a given sample size, would it be easier to detect a shift from 5% to 10% or a shift from 10% to 15%? Explain your reasoning.

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

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

__________________ variation results from causes that can be identified._

Describe the three criteria used to determine if a control chart indicates a process which is not_ statistically stable.

A teacher uses two different CAI programs to remediate a randomly selected group of students. Results for two independent samples on a standardized test are listed in a table below. At the 0.05 level of significance, use the Wilcoxon rank-sum test to test the hypothesis that the sample results are from populations with equal medians. Program I Program II 60 75 61 63 66 89 68 77 86 69 64 70 84 80 81 87 72 82 59 78 73 91 93 94 95

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. Sample Ball Bearing Diameter (mm) 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

Use the rank correlation coefficient to test for a correlation between the two variables. Given that the rank correlation coefficient, rs, for 37 pairs of data is 0.324, test the claim of correlation between the two variables. Use a significance level of 0.01.

Test the claim that the samples come from populations with the same mean. Assume that the_ populations are normally distributed with the same variance. Exercise A Exercise B Exercise 2.5 5.8 4.3 8.8 4.9 6.2 7.3 1.1 5.8 9.8 7.8 8.1 5.1 1.2 7.9 At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

Which type of chart would be best for monitoring the proportion of items that are defective?

A standard aptitude test is given to several randomly selected programmers, and the scores are given below for the mathematics and verbal portions of the test. Use the sign test to test the claim that programmers do better on the mathematics portion of the test. Use a 0.05 level of significance. start text Mathematics end text 347 440 327 456 427 349 377 398 425 start text verbal end text 285 378 243 371 340 271 294 322 385