# Ashford University Diane Vaughan Theory of Normalization of Deviance Discussion

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Lind, D. A., Marchal, W. G., & Wathen, S. A. (2017). Statistical techniques in business and economics (17th ed.). Retrieved from

The table below shows the percent of the labor force that is unemployed and the size of the labor force
for three countries in northwest Ohio. Jon Ellis is the Regional Director of Economics. He must present a
report to several companies that are:
Question 1:What would be the appropriate unemployment rate to show for the entire region? (Round
to 2 decimal places)
Percent unemployed
4.5
3.0
10.2
Size of workforce
15,300
10,400
150,600
Question 2: There are 100 employees at Kiddie. 57 are hourly worker, 40 are supervisors, 2 are
secretaries and the remaining employee is the president.
A)
B)
C)
D)
What is the probability the selected employee is an hourly worker?
What is the probability the selected employee is either an hourly worker or a supervisor?
Refer to part b . Are these events mutually exclusive?
What is the probability that neither hourly worker nor a supervisor?
Question 3: The board of directors of SAD Company consists of 12 members, 3 whom are women. A
new policy and procedure manual is to be written for the company. A committee of three is randomly
selected from the board to do the writing.
A) What is the probability that all members of the committee are men?
B) What is the probability that at least one member of the committee is a woman?
Question 4: In recent study, 35% of people surveyed indicate chocolate was their favorite flavor of ice
cream. Suppose we select a sample of ten people and ask them to name their favorite flavor of ice
cream.
How many of those in the sample would you expect to name chocolate?
B) What is the probability exactly four of those in the sample name chocolate?
A)
Question 5: Recent statistics suggest that 15 % of those who visit a retail site on the internet make a
purchase. A retailer wished to verify the claim. To do so, she selected a sample of 16 “hits” to her site
and found that 4 actually made a purchase.
A) What is the likelihood of exactly four purchases?
B) How many purchases should she expect?
Question 6: There are 10 partners in a firm. 7 live in Ohio and 3 in northern Kentucky. The owner wants
to appoint 3 partners to move to Kentucky. If the committee is selected at random from the 10 partners,
What is the probability that:
A) One member of the committee lives in northern Kentucky and the others live in Ohio?
B) At least one member of the committee loves in northern Kentucky?
Question 7: During the second round of the 1989 U.S. Open golf tournament, four golfers scored a hole
in one on the sixth hole. The odds of a professional golfer making a hole in one are estimated to be
3,708 to 1, so the probability is 1/3,709. There were 155 golfers participating in the second round that
day. Estimate the probability that 4 golfers would score a hole in one of the sixth hole.
Question 8: A) Find the median, first quartile, and third quartile for seniors
b)Find the median, first quartile, and third quartile for young adults.
28
81
35
107
41
113
48
147
52
147
81
175
97
183
98
192
98
202
99
209
118
233
132
251
133
254
140
266
145
283
147
284
153
284
158
316
162
372
174
401
177
417
180
423
180
490
187
500
188
507
518
550
557
590
594
Question 8B:A data set Consists of 83 observations. How many classes would you recommend
for a frequency distribution?
Question 9: The first row of the stem and leaf chart appears as the following 60 l 1 3 3 7 9.
Assume whole number values.
A) What is the “ Possible range“ Of the values in this row?
Question 10: Determine the median and the first and third quartiles of the following data.
46 47 49 49 51 53 54 54 55 55 59
Median:
First quartile:
Third quartile :
Question 11: The following values are the starting salaries, in \$000, For a sample of five
account and graduates who excepted positions in public accounting last year.
36.0 26.0 33.0 28.0 31.0
A) Determine the standard deviation.
B) Determine the coefficient of skewness using Pearson’s method.
C) Determine the coefficient of skewness using the software method.
Question 12: A normal distribution has a mean of 50 and a standard deviation of 4.
A) Commute the probability of a value between 44.0 and 55.0.
B)Commute the probability of a value greater than 55.0.
C) Commute the probability of a valued between 52.0 and 55.0.
Question 13: Assume a binomial probability distribution with n= 50 and π =.25 compute the
following. ( round all Z values to 2 decimal places).
b) The probability that X is 15 or more. ( Use the rounded values found above. Round your
Question 14: Recent studies indicate that the typical 50-year-old woman spends \$350 per year
for professional care products. The distribution of the amount spent follows a normal
distribution with a standard deviation of \$45 per year. We select a random sample of 40 women.
The mean amount spent for those sampled is \$335.
What is the likelihood of finding a sample mean this large or larger for the specified
population?(Round the value to two decimal places and the final answer to four decimal places)
Question 15: In the United States the mean age of men when they marry for the first time
follows a normal distribution with a mean of 29 years. The standard deviation of the distribution
is 2.5 years.
For a random sample of 60 men, what is the likelihood that the age when they were first married
is less than 29.3 years?( Round your Z value to two decimal places. Round your answer to four
decimal places)
Question 16: A new white watching company weight reducers international advertises that
those who join will lose an average of 10 pounds after the first two weeks. The standard
deviation is 2.8 pounds. A random sample of 50 people who join the weight reduction program
revealed a mean loss of 9 pounds. At the 0.05 level of significance, we can conclude that those
joining weight reducers will lose less than 10 pounds? What is a conclusion regarding the
null hypothesis?
Question 17: A recent survey by nerdwallet.com indicated Americans paid a mean of \$6,658
interest on credit card debt and 2015. A sample of 12 households with children revealed the
following amounts. 7077, 5744, 6753, 7381, 7625, 6636, 7164, 7348, 8060, 5848, 9275 ,7052.
At the 0.05 significance level is it reasonable to conclude at these households have.
At the 0.05 significance level is it reasonable to conclude at these households have more debt?
Question 18: www.gulfsmith.com reveals an average of 6.5 returns per day from online
shoppers. For a sample of 12 days, it received the following numbers of return.
0 ,4 , 3 ,4 ,9 ,4 ,5 ,9 ,1 ,6 ,7 ,10
At the 0.01 significance level, we can conclude the mean number of returns is less than 6.5?
Question 19: The number of destination weddings has skyrocketed in recent years. For example,
many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort
recently advertise the bridal magazine that because of a Caribbean where it was less than
\$30,000. Listed below is the total cost in \$000 for a sample of a Caribbean weddings. At the 0.05
significance level, is it reasonable to conclude that the main wedding cost is less than \$30,000 as
29.7 29.4 31.7 29.0 29.1 30.5 29.1 29.8
What is the conclusion regarding the null hypothesis?
Question 20: A recent study focused on the number of times men and women who lived alone
buy take out dinner in a month. Assume that a distributions to follow the normal probability
distribution and the population standard deviations are equal. The information is summarized
below.
Statistic
Sample mean
Sample standard deviation
Sample size
Men
24.51
4.48
35
Women
22.69
3.86
40
At the 0.01 significance level, is there a difference in the main number of times men and women
order takeout dinners in a month?
A) State the decision rule for 0.01 significance level: H0: μmen = μwomen
H1: μmen ≠ μwomen(round to 3 decimal places)
B)Commute the value of the test statistic. (round to 3 decimal places)
C) what is your decision regarding the null hypothesis? (fill in the blank)
The decision is __________ the null hypothesis that the means are the same.
D) what is the P value? (round to 3 decimal places)
Question 21: A real estate agent in the coastal area of Georgia wants to compare the variation
in the selling price of homes on the ocean front with those 1 to 3 blocks from the ocean. A
sample of 21 Ocean front homes sold within the last year revealed a standard deviation of the
selling price is worth \$45,600. A sample of 18 homes, also sold within the last year, that were 1
to 3 blocks from the ocean front revealed that the standard deviation was \$21,330. At the 0.01
significance level, we can conclude that there is more variation in the selling price of the ocean
homes?
1. what is a decision rule? Use the 0.01 significance level. (Round your answer to two decimal
places)
Reject H0 if F> ____
2.What is the value of F?
3. At the 0.01 significance level, we can conclude that there is more variation in the sale and
prices of the ocean front homes?
Question 22: there are two Chevrolet dealers in Jamestown New York. The main monthly sales
at Sharkley Chevy and D. White Chevrolet are about the same. However, Sharkley believes his
sales are more consistent. Below are the numbers of new car sold at Sharkley in the last 7
months and for the last 8 months at D. white. Do you agree with Sharkley? Use the 0.01
Significance level.
Sharkey
98
78
54
57
68
64
70
Dave White
75
81
81
30
82
46
58
101
1. Calculate the standard deviation for Chevy.
2. Calculate the standard deviation for a white.
3. State the decision rule for 0.01 significance level. Reject H0 if F> _______________
4.What is the value of F?
Question 22 B: In an ANOVA table, the MSE is equal to 10. Random samples of six were
selected from each of four populations, where the sum of squares total was 250.
C-1. From the information above, fill in the blanks in the table below. Round your MS to 2
decimal places. Round your other values to the nearest whole number).
Source
Treatment
Error
Total
SS
Df
MS
C-2.What is the value of F? ( Round your answer to 2 decimal places).
Question 23: Tina Dennis believes that more than 60% of the accounts are in arrears more than
3 months. A random sample of 200 I can’t show that 140 or more than three months old at the
0.01 significance level can she can close them more than 60% of the accounts are in the arrears
for more than three months?
1.State the null and alternative hypotheses.
H0:
H1:
0.60
0.60
2. Make the decision rule.
H0 is rejected if z > _________
3. Evaluate the test statistic.
4. What is a decision regarding the null hypothesis?
Question 24: Vehicles heading west on front Street may turn right, turn left, or go straight here
to Elm Street. The city traffic engineer believes that half of the vehicles will continue straight
through the intersection. Of the remaining half, equal proportions will turn right and left. 200
vehicles were observed, with the following results. Can we conclude that the traffic engineer is
correct? Use the 0.10 significance level.
Frequency
Straight
112
Right Turn
48
Left Turn
40
1. Make the decision rule. Round to three decimal places. H0 is rejected if chi-square > _______
2. Evaluate the test statistic. Round your answer to 2 decimal places
3. What is a decision regarding the null hypothesis?
Question 25: An industrial psychologist selected a random sample of 7 young urban
professional couples who own their homes. The size of their home (square feet )is compared
with that of their parents(one-tailed test).
Couple Name Professional
Gordon
1725
Sharkey
1310
Uselding
1670
Bell
1520
Kuhlman
1290
Welch
1880
Anderson
1530
Parent
1175
1120
1420
1640
1360
1750
1440
1. Complete the following table.
Couple
1
2
3
4
5
6
7
Difference
Rank
2. At 0.05 significance level, what is a Wilcoxon signed rank test value?
3. Compute the t value.
4. At the 0.05 significance level, we can conclude that the professional couples live in larger
homes and their parents?( one-tailed test)
Question 26: Eight observations were randomly selected from populations that were not
necessarily normally distributed. Use the 0.05 significance level, a two-tailed test, and the
Wilcoxon rank-sum test.
Population A
38
45
56
57
61
69
70
79
Population B
26
31
35
42
51
52
57
62
1. State the decision rule. Use the 0.05 significance level. ( Negative amounts should be indicted
2. Complete the following table.( Round your answer to 1 decimal places)
Score
38
45
56
57
61
69
70
79
Rank
0.0
B
Score
26
31
35
42
51
52
57
62
Rank
0.0
3. What is the Wilcoxon rank-sum test value ? z= _____
4. What is your decision regarding H0? Is there a difference between the two populations?
Question 27: The Vice President of programming at NBC is finalizing the prime-time schedule
for the fall. She has decided to include a hospital drama but is unsure which of two possibilities
to select. She has pilot called the Surgeon and another called Critical Care. To help her make a
final decision, a sample of 20 viewers from throughout the US was asked to watch the two pilots
and indicate which show they prefer. The results were that 12 liked The Surgeon, 7 liked Critical
Care, and one had no preference.
H0: π =0.50
H1 π ≠ 0.50
1. State the decision rule, using the 0.10 significance level.
2. What is your decision regarding H0? Is there a
preference for one of the two shows?
Question 28: The following sample observations were randomly selected.
X
4
5
3
6
10
Y
4
6
5
7
7
1. Fill in the blanks below:

ȳ
Sx
Sy
Coefficient of correlation
Coefficient of determination
2. Choose the right option.
The correlation coefficient obtained here indicates __________ correlation between X and Y.
3. Fill in the blanks.
The coefficient of determination obtained here indicated X accounts for approximately
______ percent of the variation in Y.
Question 29: The following hypotheses are given.
A random sample of 12 paired observations indicated a correlation of 0.32.
1. State the decision rule for 0.05 significance level.(Round your answer to 3 decimal places.)
2.Compute the value of the test statistic. ( Round your answer to 3 decimal places).
3. Can we conclude that the correlation in the population is greater than zero? Use the 0.05
significance level.
Question 30. And environmental protection agency study of 12 automobiles revealed a
correlation of 0.47 between engine size and emissions. We can conclude that there is a positive
association between the two variables? Use the 0.01 significance level.
Question 32: A regression analysis relating to the current market value in dollars to the size in
square feet of homes in Green county Tennessee follows. The regression equation is:
Value =-37,186+65.0 size.
Predictor
Constant
Size
Analysis of
Variance
Source
Regression
Residual Error
Total
Coef
-37186
62.993
DF
1
33
34
SE Coef
4629
3.047
T
-8.03
21.33
SS
MS
13548662082
982687392
14531349474
13548662083
29778406
P
0.000
0.000
F
454.98
P
0.000
A) how many houses were in the sample?
B) commute the standard error of estimate. (Round your answer to the nearest whole number)
C) compute the coefficient of determination.( round your answer to two decimal places)
D) Compute the correlation coefficient. (round your answer to two decimal places.)
E) at the 0.05 significance level, does the evidence suggest a positive association between the
market value of homes and the size of the home in square feet? Fill in the blanks.
_______ , because the t-value is ________ the critical value and the p-value is _______ the
significance level.
Question 33: The director of marketing of Reeves wholesale products is studying monthly sales.
Three independent variables were selected as estimators of sales: region of population, per
capita income, and regional unemployment rate. The regression equation was computed to be
(in dollars):
y= 64,100+0.394×1 + 9.6×2 – 11,600×3
Note : Here, the variables x1, x2, x3 refer to regional population, Per capita income, and regional
unemployment rate respectively.
C. What are the estimated monthly sales for a particular region with a population of \$796,000
per capita income of \$6,940, and an unemployment rate of 6.0%?
Question 34: A consulting group was hired by the human resources department at General
Mills Inc. to survey company employees regarding there their degree of satisfaction with their
quality-of-life. A special index, called the index of satisfaction, was used to measure six factors
were studied, namely, age at the time of first marriage(x1), annual income(x2), number of
children(x3), value of all assets(x4), status of health and the form of an index(x5), and the
average number of social activities per week(x6) such as bowling and dancing. Suppose a
multiple regression equation is: y= 16.24 + 0.017×1 + 0.0028×2 + 42×3 + 0.0012×4 + 0.19×5 +
26.8×6
B) Which will add more to satisfaction, an additional income of \$10,000 a year or two more
social activities a week?
Question 35: The owner of egg form wants to estimate the main number of eggs produced per
chicken. A sample of 20 chickens shows they produce an average of 20 eggs per month with a
standard deviation of two eggs per month. ( Use t-distribution table)
D) developed the 95% confidence interval for the population mean. Round your answer to two
decimal places
Confidence interval ____ to ______
Question 36: The owner of West end gas station wishes to determine the proportion of
customers who pay at the pump using a credit card or debit card. He surveys 100 customers and
five that 80 paid at the pump (round your answers to two decimal places.)
A)Estimate the value of the population proportion
B) develop a 95% confidence interval of the population proportion
Question 37: A random sample of 400 viewers were selected and asked to watch the new
comedy show and the crime investigation show at the view in the shows, 250 indicated they
would watch a new comedy show and suggested it replace the criminal investigation show.
A) estimate the value of the population proportion
B) determine the 99% confidence interval for the population proportion
Question 38: A population standard deviation is 10. We want to estimate the population mean
within 2, with a 95% level of confidence.
How large a sample is required? Round up your answer to the next whole number
Question 39: The estimate of the population proportion should be within plus or minus .05,
with a 95% level of confidence. The best estimate of the population proportion is .15. How large
a sample is required? Use t- distribution table ( Round Z value to two decimal places and round
Question 41: WRI advertise that those who join will lose an average of 10 pounds after the first
two weeks. The standard deviation is 2.8 pounds. A random sample of 50 people who joined the
weight reduction program revealed a mean loss of 9 pounds. At the 0.05 level of significance, we
can conclude that those joining will lose an average of 10 pounds after the first two weeks.
Question 42: A recent study focus on the number of times men and women who live alone but
take out dinner in a month. Assume that the distributions follow the normal probability
distribution and the population standard deviations are equal. The information is summarized
below. Develop an effective size measure (round to two decimal places)
Statistic
Sample mean
Sample standard deviation
Sample size
Men
24.51
4.48
35
Women
22.69
3.86
40
Question 43: In an ANOVA table, the MSE is equal to 10. Random samples of six seats were
selected from each of four populations, where the sum of squares total was 250. Developed an
effect size measure for Chapter 12 question 27. (Round to two decimal places)
Question 44: Vehicles heading west on front Street may turn right, turn left, or go straight here to
Elm Street. The city traffic engineer believes that half of the vehicles will continue straight
through the intersection. Of the remaining half, equal proportions will turn right and left. 200
vehicles were observed, with the following results. Can we conclude that the traffic engineer is
correct? Use the 0.10 significance level.
Frequency
Straight
112
Right Turn
48
Question 45: The following sample observations were randomly selected.
X
4
5
3
6
10
Y
4
6
5
7
7
Left Turn
40