Question 1

$\text { Construct an } \bar{x} \text { chart and determine whether the process variation is within statistical contro }$
$\text { Control Chart Constants }$
$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$ \bar{x} $ $  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $    $ \boldsymbol{s} $  $  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $ $ \boldsymbol{R} $
$\begin{array}{ccccccc}
\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \
\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \
3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \
4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \
5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \
6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \
7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \
8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \
9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \
10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \
\hline
\end{array}$

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.
 $  \quad $ $  \quad $ $  \quad $ $  \quad $ $  \quad $$\text { Ball Bearing Diameter }(\mathrm{mm} \text { ) }$
$\begin{array}{c|ccccc|c|c|}
\text { Sample } &&&&& & \bar{x} & \text { Range } \
\hline 1 & 6.3 & 6.8 & 6.9 & 6.8 & 6.9 & 6.74 & 0.6 \
2 & 6.3 & 6.6 & 6.6 & 6.3 & 7.0 & 6.56 & 0.7 \
3 & 6.8 & 6.7 & 7.0 & 6.5 & 7.0 & 6.80 & 0.5 \
4 & 7.0 & 6.7 & 6.7 & 6.8 & 6.8 & 6.80 & 0.3 \
5 & 6.8 & 6.8 & 6.6 & 6.5 & 6.4 & 6.62 & 0.4 \
6 & 6.8 & 6.7 & 6.6 & 6.3 & 6.9 & 6.66 & 0.6 \
7 & 7.3 & 7.3 & 7.4 & 7.4 & 7.0 & 7.28 & 0.4 \
8 & 7.2 & 7.0 & 7.2 & 6.9 & 7.1 & 7.08 & 0.3 \
9 & 7.3 & 7.6 & 7.1 & 7.4 & 7.6 & 7.40 & 0.5 \
10 & 7.2 & 7.6 & 7.5 & 7.6 & 7.1 & 7.40 & 0.5 \
11 & 7.2 & 7.2 & 7.4 & 7.0 & 7.0 & 7.16 & 0.4 \
12 &  \quad7.5  \quad& 7.4 & 7.4 & 7.6 & \quad 7.1  \quad& 7.40 & 0.5
\end{array}$

Accepted Answer

The answer of \(\text { Construct an } \bar{x} \text...

Question 2

The
values are given. Is there a significant effect from the interaction? Should you test to see if
there is a significant effect due to either A or B? If the answer is yes, is there a significant
effect due to either A or B? $\begin{array}{c|r|r|r|r|r}
\text { Source } & \text { DF } & \text { Sum squares } & \text { Mean square } & \text { F test } & \text { P-value } \
\hline \text { A } & 2 & 164.020 & 82.010 & 25.010 & <.0001 \
\text { B } & 4 & 230.786 & 57.697 & 18.002 & <.0001 \
\text { Interaction Error Total } & 8 & 80.879 & 10.110 & 3.154 & .0031 \
& 101 & 323.708 & 3.205 & & \
& 115 & 799.393 & & &
\end{array}$

Accepted Answer

The answer of The
values are given. Is there a significant...

Question 3

The data below represent the weight losses for people on three diets. $\begin{array}{lcc}
\text { Diet A } & \text { Diet B } & \text { Diet C } \
\hline 1.75 & 3.8 & 4.8 \
8.8 & 4.9 & 6.2 \
7.3 & 1.1 & 5.8 \
9.8 & 7.8 & 8.1 \
5.1 & 1.2 & 6.9
\end{array}$

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 $\mu _ { 1 } = \mu _ { 3 }$ ?

Accepted Answer

The answer of The data below represent the weight losses...

Question 4

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?

Accepted Answer

The answer of If test A has an efficiency rating...

Question 5

The following data contains task completion times, in minutes, categorized according to the
gender of the machine operator and the machine used. $$\begin{array} { l c c } 
& \text { Male } & \text { Female } \
\text { Machine 1 } & 15,17 & 16,17 \
\text { Machine 2 } & 14,13 & 15,13 \
\text { Machine 3 } & 16,18 & 17,19
\end{array}$$ Assume that two-way ANOVA is used to analyze the data. How are the ANOVA results
affected if 5 minutes is added to each completion time?

Accepted Answer

The answer of The following data contains task completion times,...

Question 6

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?

Accepted Answer

The answer of Test the claim that the samples come...

Question 7

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 between percentage of vote and income level at the $0.01$ significance level with a null hypothesis of $\rho _ { s } = 0$.

Accepted Answer

A)  The test statistic is between the critical values, so we fail to reject the null hypothesis. There is no evidence to support a claim of correlation between percentage of vote and income level. 
B)  The test statistic is not between the critical values, so we fail to reject the null hypothesis. There is no evidence to support a claim of correlation between percentage of vote and income level. 
C)  The test statistic is between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level. 
D)  The test statistic is not between the critical values, so we reject the null hypothesis. There is sufficient evidence to support a claim of correlation between percentage of vote and income level.

Question 8

$\text { Construct an } \bar{x} \text { chart. }$
$\text { Control Chart Constants }$
$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$ \bar{x} $ $  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $    $ \boldsymbol{s} $  $  \quad $$  \quad $$  \quad $$  \quad $$  \quad $$  \quad $ $ \boldsymbol{R} $
$\begin{array}{ccccccc}
\hline n & A_{2} & A_{3} & B_{3} & B_{4} & D_{3} & D_{4} \
\hline 2 & 1.880 & 2.659 & 0.000 & 3.267 & 0.000 & 3.267 \
3 & 1.023 & 1.954 & 0.000 & 2.568 & 0.000 & 2.574 \
4 & 0.729 & 1.628 & 0.000 & 2.266 & 0.000 & 2.282 \
5 & 0.577 & 1.427 & 0.000 & 2.089 & 0.000 & 2.114 \
6 & 0.483 & 1.287 & 0.030 & 1.970 & 0.000 & 2.004 \
7 & 0.419 & 1.182 & 0.118 & 1.882 & 0.076 & 1.924 \
8 & 0.373 & 1.099 & 0.185 & 1.815 & 0.136 & 1.864 \
9 & 0.337 & 1.032 & 0.239 & 1.761 & 0.184 & 1.816 \
10 & 0.308 & 0.975 & 0.284 & 1.716 & 0.223 & 1.777 \
\hline
\end{array}$

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.
 $  \quad $ $  \quad $ $  \quad $ $  \quad $ $  \quad $$\text { Box Weight (lb) }$
$\begin{array}{l}
\begin{array}{c|}
\underline {\text { Sample } }\
 1\
2\
3\
4\
5\
6\
7\
8\
9\
10\
11\
12\
13\
14\
15\
\end{array}
\begin{array}{lrll|}
\
\hline 49 & 38 & 39 & 45 \
52 & 51 & 43 & 61 \
56 & 60 & 32 & 52 \
44 & 59 & 46 & 49 \
51 & 61 & 48 & 45 \
45 & 50 & 46 & 48 \
52 & 51 & 45 & 55 \
40 & 50 & 53 & 48 \
48 & 67 & 60 & 51 \
43 & 50 & 50 & 47 \
48 & 30 & 38 & 39 \
50 & 46 & 48 & 53 \
50 & 58 & 56 & 64 \
47 & 52 & 47 & 49 \
52 & 57 & 58 & 52
\end{array}
\begin{array}{c|}
\bar{x} \
\hline 42.75 \
51.75 \
50.00 \
49.50 \
51.25 \
47.25 \
50.75 \
47.75 \
56.50 \
47.50 \
38.75 \
49.25 \
57.00 \
48.75 \
54.75
\end{array}
\begin{array}{c}
\text { Range } \
\hline 11 \
18 \
28 \
15 \
16 \
5 \
10 \
13 \
19 \
7 \
18 \
7 \
14 \
5 \
6
\end{array}
\end{array}$

Accepted Answer

The answer of \(\text { Construct an } \bar{x} \text...

Question 9

Use a 0.05 level of significance to test the claim that the sequence of computer -generated
numbers is random. Test for randomness above and below the mean. $$8757391804384623975$$

Accepted Answer

The answer of Use a 0.05 level of significance to...

Question 10

Use the sign test to test the indicated claim. An instructor gives a test before and after a lesson
and results from randomly selected students are given below. At the 0.05 level of significance,
test the claim that the lesson has no effect on the grade. Use the sign test. $$\begin{array} { l l l l l l l l l l l l l l l l } 
\text { Before } & 54 & 61 & 56 & 41 & 38 & 57 & 42 & 71 & 88 & 42 & 36 & 23 & 22 & 46 & 51 \
\hline \text { After } & 82 & 87 & 84 & 76 & 79 & 87 & 42 & 97 & 99 & 74 & 85 & 96 & 69 & 84 & 79
\end{array}$$

Accepted Answer

The answer of Use the sign test to test the...

Question 11

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. $$\begin{array} { c c c } 
\text { Brand A } & \text { Brand B } & \text { Brand } \mathbf { C } \
\hline 32 & 27 & 22 \
34 & 24 & 25 \
37 & 33 & 32 \
33 & 30 & 22 \
36 & & 21 \
39 & &
\end{array}$$

Accepted Answer

The answer of Test the claim that the samples come...

Question 12

Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4,
5, 5, 5, 7, 8, 12, 12, 15, 18).

Accepted Answer

The answer of Define rank. Explain how to find the...

Question 13

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. $$\begin{array} { c c c c c c c c c c c c } 
\text { College A } & 3.2 & 4.0 & 2.4 & 2.6 & 2.0 & 1.8 & 1.3 & 0.0 & 0.5 & 1.4 & 2.9 \
\hline \text { College B } & 2.4 & 1.9 & 0.3 & 0.8 & 2.8 & 3.0 & 3.1 & 3.1 & 3.1 & 3.5 & 3.5
\end{array}$$

Accepted Answer

The answer of Use the Wilcoxon rank-sum approach to test...

Question 14

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.
What would be the value of the centerline that would be used in creating an R chart?  $  \quad $  $  \quad $  $  \quad $  $  \quad $ $\text { Box Weight (Ib) }$
$\begin{array}{|c|cccc|c}
\text { Sample }&&&&&\bar{x}\
\hline 1 & 49 & 38 & 39 & 45 & 42.75 \
2 & 52 & 51 & 43 & 61 & 51.75 \
3 & 56 & 60 & 32 & 52 & 50.00 \
4 & 44 & 59 & 46 & 49 & 49.50 \
5 & 51 & 61 & 48 & 45 & 51.25 \
6 & 45 & 50 & 46 & 48 & 47.25 \
7 & 52 & 51 & 45 & 55 & 50.75 \
8 & 40 & 50 & 53 & 48 & 47.75 \
9 & 48 & 67 & 60 & 51 & 56.50 \
10 & 43 & 50 & 50 & 47 & 47.50 \
11 & 48 & 30 & 38 & 39 & 38.75 \
12 & 50 & 46 & 48 & 53 & 49.25 \
13 & 50 & 58 & 56 & 64 & 57.00 \
14 & 47 & 52 & 47 & 49 & 48.75 \
15 & 52 & 57 & 58 & 52 & 54.75
\end{array}$

Accepted Answer

A)  $49.567 \text { pounds }$ 
B)  $50 \text { pounds }$ 
C)  $11.000 \text { pounds }$ 
D)  $12.8000\text { pounds }$

Question 15

Use the data in the given table and the corresponding Minitab display to test the hypothesis.
The following table shows the mileage for four different cars and three different brands of
gas. Assuming no effect from the interaction between car and brand of gas, test the claim
that the four cars have the same mean mileage. Use a 0.05 significance level. $\begin{array}{l|lll} 
& \text { Brand 1 } & \text { Brand 2 } & \text { Brand 3 } \
\hline \text { Car 1 } & 22.4 & 25.2 & 24.3 \
\text { Car 2 } & 19 & 18.6 & 19.8 \
\text { Car 3 } & 24.6 & 25 & 25.4 \
\text { Car 4 } & 23.5 & 23.6 & 24.1
\end{array}$

$\begin{array}{lrcrrc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { p } \
\text { Car } & 3 & 61.249 & 20.416 & 39.033 & 0.000249 \
\text { Gas } & 2 & 2.222 & 1.111 & 2.124 & 0.200726 \
\text { Error } & 6 & 3.138 & 0.523 & & \
\text { Total } & 11 & 66.609 & & &
\end{array}$

Accepted Answer

The answer of Use the data in the given table...

Question 16

Use the given process data to construct a control chart for p. If the weight of cereal in a
particular packet is less than 14 ounces, the packet is considered nonconforming. Each week,
the manufacturer randomly selects 1,000 cereal packets and determines the number that are
nonconforming. The results for 12 consecutive weeks are shown below. $$\begin{array} { l l l l l l l l l l l l } 
46 & 32 & 21 & 30 & 47 & 31 & 32 & 52 & 48 & 45 & 62 & 58
\end{array}$$

Accepted Answer

The answer of Use the given process data to construct...

Question 17

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. $$\begin{array} { l l l l l l l l l l l l } 
4 & 7 & 5 & 6 & 8 & 3 & 12 & 4 & 4 & 5 & 6 & 2
\end{array}$$

Accepted Answer

The answer of Use the given process data to construct...

Question 18

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

Accepted Answer

A)  $R$ chart 
B)  $\bar { x }$ chart 
C)  $p$ chart 
D)  Run chart

Question 19

Which of the following is not an application of the sign test?

Accepted Answer

A)  Test claims involving matched pairs 
B)  Test claims involving nominal data 
C)  Test claims about the median of a single population 
D)  Test claims about correlation

Question 20

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

Accepted Answer

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

Exam 12: Control Charts and Process Monitoring

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?

Use a 0.05 level of significance to test the claim that the sequence of computer -generated numbers is random. Test for randomness above and below the mean. $8757391804384623975$

Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4, 5, 5, 5, 7, 8, 12, 12, 15, 18).

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

Which of the following is not an application of the sign test?

Exam 12: Control Charts and Process Monitoring

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?

Use a 0.05 level of significance to test the claim that the sequence of computer -generated numbers is random. Test for randomness above and below the mean. 875739180438462397587573918043846239758757391804384623975

Define rank. Explain how to find the rank for data which repeats (for example, the data set: 4, 5, 5, 5, 7, 8, 12, 12, 15, 18).

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

Which of the following is not an application of the sign test?

Use a 0.05 level of significance to test the claim that the sequence of computer -generated numbers is random. Test for randomness above and below the mean. $8757391804384623975$