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 value of the test statistic. $\begin{array}{l|r|c|c|c|c} \text { Source } & \boldsymbol{D F} & \boldsymbol{S S} & \boldsymbol{M S} & \boldsymbol{F} & \boldsymbol{p} \\ \hline \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \\ \hline \text { Error } & 16 & 13.925 & 0.870 & & \\ \hline \text { Total } & 19 & 27.425 & & & \end{array}$

A) $5.17$ B) $4.500$ C) $13.500$ D) $0.011$ A) $5.17$ B) $4.500$ C) $13.500$ D) $0.011$

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. The data below represent the weight losses for people on three different exercise programs. \[\begin{array} { c c c } \text { Exercise A } & \text { Exercise B } & \text { Exercise C } \\ \hline 2.5 & 5.8 & 4.3 \\ 8.8 & 4.9 & 6.2 \\ 7.3 & 1.1 & 5.8 \\ 9.8 & 7.8 & 8.1 \\ 5.1 & 1.2 & 7.9 \end{array}\] At the 1% significance level, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

Test statistic: F = 1.491. Critical valu

Fill in the missing entries in the following partially completed one -way ANOVA table._ $\begin{array}{l|c|c|c|c} \text { Source } & d f & S S & M S=S S / d f & F \text {-statistic } \\ \hline \text { Treatment } & 3 & & & 11.16 \\ \hline \text { Error } & & 13.72 & 0.686 & \\ \hline \text { Total } & & & & \end{array}$

A) $\begin{array}{l|c|c|c|c} \text { Source } & d f & S S & M S=S S / d f & F \text {-statistic } \\ \hline \text { Treatment } & 3 & 22.97 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 36.69 & & \end{array}$ B) $\begin{array}{l|c|c|c|c} \text { Source } & \boldsymbol{d f} & \boldsymbol{S S} & \boldsymbol{M S}=\boldsymbol{S S} / d \boldsymbol{f} & \boldsymbol{F} \text {-statistic } \\ \hline \text { Treatment } & 3 & 2.55 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 16.27 & & \end{array}$ C) $\begin{array}{l|c|c|c|c} \text { Source } & \boldsymbol{d f} & \boldsymbol{S S} & \boldsymbol{M S}=\boldsymbol{S S} / \mathrm{df} & \boldsymbol{F} \text {-statistic } \\ \hline \text { Treatment } & 3 & 48.80 & 16.27 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 62.52 & & \end{array}$ D) $\begin{array}{l|c|c|c|c} \text { Source } & \boldsymbol{d} \boldsymbol{f} & \boldsymbol{S S} & \boldsymbol{M S}=\boldsymbol{S S} / \mathrm{df} & \boldsymbol{F} \text {-statistic } \\ \hline \text { Treatment } & 3 & 0.184 & 0.061 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 13.90 & & \end{array}$ A) $\begin{array}{l|c|c|c|c} \text { Source } & d f & S S & M S=S S / d f & F \text {-statistic } \\ \hline \text { Treatment } & 3 & 22.97 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 36.69 & & \end{array}$ B) $\begin{array}{l|c|c|c|c} \text { Source } & \boldsymbol{d f} & \boldsymbol{S S} & \boldsymbol{M S}=\boldsymbol{S S} / d \boldsymbol{f} & \boldsymbol{F} \text {-statistic } \\ \hline \text { Treatment } & 3 & 2.55 & 7.66 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 16.27 & & \end{array}$ C) $\begin{array}{l|c|c|c|c} \text { Source } & \boldsymbol{d f} & \boldsymbol{S S} & \boldsymbol{M S}=\boldsymbol{S S} / \mathrm{df} & \boldsymbol{F} \text {-statistic } \\ \hline \text { Treatment } & 3 & 48.80 & 16.27 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 62.52 & & \end{array}$ D) $\begin{array}{l|c|c|c|c} \text { Source } & \boldsymbol{d} \boldsymbol{f} & \boldsymbol{S S} & \boldsymbol{M S}=\boldsymbol{S S} / \mathrm{df} & \boldsymbol{F} \text {-statistic } \\ \hline \text { Treatment } & 3 & 0.184 & 0.061 & 11.16 \\ \hline \text { Error } & 20 & 13.72 & 0.686 & \\ \hline \text { Total } & 23 & 13.90 & & \end{array}$

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

If test A has an efficiency rating of 0.94 as compared to test B, explain what that efficiency rating means. Do comparable nonparametric or parametric tests have higher efficiency ratings?

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Question 1

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Higher efficiency ratings have the effect that "significant" results typically require smaller samples. For example if
test A has an efficiency rating of 0.94 as compared to test B, that means that test A requires 100 sample
observations as compared to 94 sample observations for test B. Parametric tests have higher efficiency ratings.

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.

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Random variation is due to chance, the variation inherent in any process that is not capable of producing each good
or service exactly the same way every time. Assignable variation results from causes that can be identified.
Examples may vary.

Describe a p chart and give an example.

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A p chart is a sequential plot of proportions of some process attribute over time. The horizontal axis is used for time,
and the vertical axis is used for the proportions of that attribute of the samples. Examples will vary. A p chart
attempts to monitor the proportion of a particular attribute.

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

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Question 4

Use the Wilcoxon rank-sum test to test the claim that the two independent samples come from populations with equal medians. Use the Wilcoxon rank-sum approach to test the claim that the sample student grade averages at two colleges come from populations with the same median. 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

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Question 5

One way analysis of variance is used to test for _________________________________.

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Question 6

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

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Question 7

Select a property of the F distribution.

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Question 8

Use the given process data to construct a control chart for p. A candy manufacturer considers a cracked piece of candy to be a defect. Each day 100 candies are randomly selected and Checked for cracks. The numbers of defects for 20 consecutive days are given below. 14 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 center line?

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Question 9

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 value of the test statistic. Source Factor 3 13.500 4.500 5.17 0.011 Error 16 13.925 0.870 Total 19 27.425

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Question 10

Use the sign test to test the indicated claim. The waiting times (in minutes)of 28 randomly_ selected customers in a bank are given below. Use a significance level of 0.05 to test the claim that the population median is equal to 5.3 minutes. 8.2 8.0 10.5 3.8 6.4 5.3 7.8 2.9 6.0 7.7 6.1 5.9 1.2 10.4 7.3 6.9 5.8 5.1 6.2 3.1 5.8 11.7 4.5 6.5 9.8 7.4 2.3 7.8

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Question 11

Match the chart with its characteristic. -The centerline is $\bar { x }$

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Question 12

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. The data below represent the weight losses for people on three different exercise programs. Exercise A Exercise B Exercise C 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?

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Question 13

Sketch a run chart that that indicates that a process is not statistically stable due to increasing variation.

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Question 14

Use the given process data to construct a control chart for p. A manufacturer monitors the level_ of defects in the television sets that it produces. Each week, 200 television sets are randomly selected and tested and the number of defects is recorded. The results for 12 consecutive weeks are shown below. 4 7 5 6 8 3 12 4 4 5 6 2

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Question 15

At the same time each day, a researcher records the temperature in each of three greenhouses. The table shows the temperatures in degrees Fahrenheit recorded for one week. Greenhouse \#1 Greenhouse \#2 Greenhouse \#3 73 71 67 72 69 63 73 72 62 66 72 61 68 65 60 71 73 62 72 71 59 i)Use a 0.05 significance level to test the claim that the average temperature is the same in each greenhouse. ii)How are the analysis of variance results affected if the same constant is added to every one of the original sample values?

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Question 16

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 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 A) $0.264$ В) $10.00$ C) $6.25$ D) $1.6$

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Question 17

When applying the runs test for randomness above and below the median for 10 scores on a final exam, the test statistic is G = 2. What does that value tell us about the data?

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Question 18

Match the chart with its characteristic. -It has no upper or lower control limits.

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Question 19

Fill in the missing entries in the following partially completed one -way ANOVA table._ Source df SS MS=SS/df F -statistic Treatment 3 11.16 Error 13.72 0.686 Total

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Question 20

If test A has an efficiency rating of 0.94 as compared to test B, explain what that efficiency rating means. Do comparable nonparametric or parametric tests have higher efficiency ratings?

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.

Describe a p chart and give an example.

One way analysis of variance is used to test for _________________________________.

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

Select a property of the F distribution.

Match the chart with its characteristic. -The centerline is $\bar { x }$

Sketch a run chart that that indicates that a process is not statistically stable due to increasing variation.

When applying the runs test for randomness above and below the median for 10 scores on a final exam, the test statistic is G = 2. What does that value tell us about the data?

Match the chart with its characteristic. -It has no upper or lower control limits.

Fill in the missing entries in the following partially completed one -way ANOVA table._ Source df SS MS=SS/df F -statistic Treatment 3 11.16 Error 13.72 0.686 Total

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Filters

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

If test A has an efficiency rating of 0.94 as compared to test B, explain what that efficiency rating means. Do comparable nonparametric or parametric tests have higher efficiency ratings?

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.

Describe a p chart and give an example.

A control chart for xˉ\bar { x }xˉ 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 rejection of a statistically stable mean.

One way analysis of variance is used to test for _________________________________.

When applying the runs test for randomness above and below the median for 12 dollar/Euro exchange rate highs, the test statistic is G = 2. What does that value tell us about the data?

Select a property of the F distribution.

Match the chart with its characteristic. -The centerline is xˉ\bar { x }xˉ

Sketch a run chart that that indicates that a process is not statistically stable due to increasing variation.

When applying the runs test for randomness above and below the median for 10 scores on a final exam, the test statistic is G = 2. What does that value tell us about the data?

Match the chart with its characteristic. -It has no upper or lower control limits.

Fill in the missing entries in the following partially completed one -way ANOVA table._ Source df SS MS=SS/df F -statistic Treatment 3 11.16 Error 13.72 0.686 Total

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Normal Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Filters

Match the chart with its characteristic. -The centerline is $\bar { x }$