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

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 What is the value of the upper control limit?

Consider process data consisting of the amounts of potato chips (in ounces)in randomly selected bags of chips. The process is to be monitored with $\bar { x }$ control charts based on samples Of 50 bags randomly selected each day for 15 consecutive days of production. What does X Denote?

The following scatterplot shows the percentage of the vote a candidate received in the 2004_ senatorial elections according to the voter's income level based on an exit poll of voters Conducted by CNN. The income levels 1 -8 correspond to the following income classes: 1 =Under $15,000; 2 =$15-30,000; 3=$30-50,000; 4=$50-75,000; 5=$75-100,000; 6=$100- 150,000; 7=$150-200,000; 8=$200,000 or more. Use the election scatterplot to determine whether there is a correlation bet ween percentage of Vote and income level at the 0.01 significance level with a null hypothesis of ρs = 0.

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.

Examine the given run chart or control chart and determine whether the process is within statistical control.

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. n=30 , $\alpha = 0.05$

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean and range (in hours)of the lifetimes of the 10 lightbulbs are calculated. The results for 12 consecutive days are shown in the table below. Construct an R chart to determine whether The process is in statistical control. Day Range s 1 201.1 3.4 1.2 2 203.4 4.7 1.7 3 200.9 3.1 0.9 4 205.6 6.2 2.3 5 201.3 4.7 1.3 6 200.5 3.7 1.7 7 205.8 5.8 2.1 8 203.7 6.2 2.9 9 199.8 2.1 0.8 10 202.7 4.4 1.6 11 200.0 2.7 0.7 12 204.6 7.8 3.0 $\text { Control Chart Constants }$ 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

Find the ranks corresponding to the ages of five statistics professors when they were hired:_ 47, 51, 47, 47, 48

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.

Describe an R chart and give an example. What does it attempt to monitor?

The data below represent the weight losses for people on three different exercise programs. 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 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 $\mu _ { 1 } = \mu _ { 3 }$ ?

Sketch a control chart that indicates that a process is not statistically stable due to the run of 8 rule.

Use the Minitab display to test the indicated claim. A manager records the production output of_ three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow. Employee A B C Machine I 31,34,32 29,23,22 21,20,24 II 19,26,22 35,33,30 25,19,23 III 21,18,26 20,23,24 36,37,31 ANALYSIS OF VARIANCE ITEMS SOURCE DF SS MS MACHINE 2 1.19 .59 EMPLOYEE 2 5.85 2.93 INTERACTION 4 710.81 177.70 ERROR 18 160.00 8.89 TOTAL 26 877.85 Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced.

Use the runs test to determine whether the given sequence is random. Use a significance level of 0.05. A sample of 30 clock radios is selected in sequence from an assembly line. Each radio is examined and judged to be acceptable (A)or defective (D). The results are shown below. Test for randomness. A A D A A A D A A D A D A A A D A A A A A A D D A A A A D A

What is the corresponding parametric test for the Kruskal-Wallis test?

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

Select an appropriate null hypothesis for a one way analysis of variance test. A) $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \mu _ { 3 } = \mu _ { 4 }$ B) $H _ { 0 } : \mu _ { 1 } \neq \mu _ { 2 } \neq \mu _ { 3 } \neq \mu _ { 4 }$ C) $H _ { 0 } : p _ { 1 } \neq p _ { 2 } \neq p _ { 3 } \neq p _ { 4 }$ D) $H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 } = \sigma _ { 3 } = \sigma _ { 4 }$

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.

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. What can you conclude about the equality of the Population means? Source Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

Use the sign test to test the indicated claim. The heights of 16 randomly selected women are given below. Use a significance level of 0.05 to test the claim that the population median is equal to 64.0 inches. 62.9 61.9 66.4 68.5 63.7 64.0 65.2 67.0 70.2 65.3 64.0 60.3 64.3 66.9 65.0 63.8