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1. The following ANOVA table was obtained when estimating a multiple regression.
ANOVA
Regression
Residual
df
2
15
SS
188,691.90
45,499.10
Total
17
234,191.00
MS
F
94,345.95 31.10
3,033.27
Significance F
4.61E-06
A) Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
B) Calculate the coefficient of determination. (Round your answer to 4 decimal places.)
C) Interpret the coefficient of determination. Please select one of the following.
C1)The proportion of the variation in x that is explained by the regression model.
C2) The proportion of the variation in y that is explained by the regression model.
D) Calculate adjusted R2. (Round your answer to 4 decimal places.)
2. A random variable X is exponentially distributed with a mean of 0.21.
A) What is the rate parameter λ? (Round your answer to 3 decimal places.)
B) What is the standard deviation of X? (Round your answer to 3 decimal places.)
C) Compute P(X > 0.36). (Round intermediate calculations to 4 decimal places and final answer to 4
decimal places.)
D) Compute P(0.21 ≤ X ≤ 0.36). (Round intermediate calculations to 4 decimal places and final answer to
4 decimal places.)
3. Complete the following probability table. (Round Prior Probability answers to 2 decimal places and
intermediate calculations and other answers to 4 decimal places.)
y-hat
4. Consider the following hypotheses:
H0: μ = 39
HA: μ ≠ 39
The population is normally distributed. A sample produces the following observations:
39
40
44
38
40
41
44
Use the p-value approach to conduct the test at a 5% level of significance. Use Table 2. Also, use Excel
data file titled “Question 4.”
A) Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places.
Round your answers to 2 decimal places.)
B) Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places. Round
your answer to 2 decimal places.)
C) Approximate the p-value of the test statistic. Please select one of the following.
C1) 0.02 < p-value < 0.05
C2) 0.05 < p-value < 0.10
C3) p-value < 0.02
D) What is the conclusion? Please select one of the following.
D1) Reject H0 since the p-value is [a(30)] than α.
D2) Reject H0 since the p-value is [a(31)] than α.
D3) Do not reject H0 since the p-value is [a(30)] than α.
D4) Do not reject H0 since the p-value is [a(31)] than α.
5. A machine that is programmed to package 3.28 pounds of cereal is being tested for its accuracy. In a
sample of 49 cereal boxes, the sample mean filling weight is calculated as 3.28 pounds. It can be
assumed that filling weights are normally distributed with a population standard deviation of 0.13
pound. Use Table 1.
A) Identify the relevant parameter of interest for these quantitative data. Please select one of the
following.
A1)The parameter of interest is the proportion filling weight of all cereal packages.
A2)The parameter of interest is the average filling weight of all cereal packages.
B) Compute the point estimate as well as the margin of error with 95% confidence. (Round intermediate
calculations to 4 decimal places. Round "z" value and final answers to 2 decimal places.)
C) Calculate the 95% confidence interval. (Use rounded margin of error. Round your answers to 2
decimal places.)
Confidence interval
?
to
?
D) Can we conclude that the packaging machine is operating improperly? Please select one of the
following.
D1) Yes, since the confidence interval contains the target filling weight of 3.28.
D2) Yes, since the confidence interval does not contain the target filling weight of 3.28.
D3) No, since the confidence interval contains the target filling weight of 3.28.
D4) No, since the confidence interval does not contain the target filling weight of 3.28.
E) How large a sample must we take if we want the margin of error to be at most 0.02 pound with 95%
confidence? (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places
and round up your final answer to the next whole number.)
6. In a multiple regression with two explanatory variables and 118 observations, it is found that SSR =
4.63 and SST = 7.95.
A) Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
B) Calculate the coefficient of determination R2. (Round your answer to 4 decimal places.)
C) Calculate adjusted R2. (Round your answer to 4 decimal places.)
7. Market observers are quite uncertain whether the stock market has bottomed out from the economic
meltdown that began in 2008. In an interview on March 8, 2009, CNBC interviewed two prominent
economists who offered differing views on whether the U.S. economy was getting stronger or weaker.
An investor not wanting to miss out on possible investment opportunities considers investing $20,000 in
the stock market. He believes that the probability is 0.23 that the market will improve, 0.47 that it will
stay the same, and 0.30 that it will deteriorate. Further, if the economy improves, he expects his
investment to grow to $27,000, but it can also go down to $17,000 if the economy deteriorates. If the
economy stays the same, his investment will stay at $20,000.
A) What is the expected value of his investment?
B) What should the investor do if he is risk neutral?
Investor SHOULD or SHOULD NOT invest the $20,000.
C) Is the decision clear-cut if he is risk averse?
YES or NO.
8. At a local bar in a small Midwestern town, beer and wine are the only two alcoholic options. The
manager noted that of all male customers who visited over the weekend, 160 ordered beer, 33 ordered
wine, and 35 asked for soft drinks. Of female customers, 46 ordered beer, 24 ordered wine, and 17
asked for soft drinks.
A) Construct a contingency table that shows frequencies for the qualitative variables Gender (male or
female) and Drink Choice (beer, wine, or soft drink).
Gender
Male (M)
Female (F)
Total
Beer (B)
?
?
?
Drink Choice
Wine (W)
?
?
?
Soft Drinks (D)
?
?
?
Total
?
?
?
B) Find the probability that a customer orders wine. (Round your intermediate calculations and final
answer to 4 decimal places.)
C) What is the probability that a male customer orders wine? (Round your intermediate calculations and
final answer to 4 decimal places.)
D) Are the events “Wine” and “Male” independent? Please select one of the following.
D1) Yes because P(“Wine” | “Male”) = P(“Wine”).
D2) Yes because P(“Wine” ∩ “Male”) = P(“Wine”).
D3) No because P(“Wine” | “Male”) ≠ P(“Wine”).
D4) No because P(“Wine” ∩ “Male”) ≠ P(“Wine”).
9) A manager of a local retail store analyzes the relationship between advertising and sales by reviewing
the store’s data for the previous six months.
Advertising (in $100s)
155
54
53
52
193
191
Sales (in $1,000s)
125
42
41
40
117
115
Use excel data file titled “Question 9”
A) Calculate the mean of advertising and the mean of sales. (Round your answers to 2 decimal places.)
B) Calculate the standard deviation of advertising and the standard deviation of sales. (Round your
answers to 2 decimal places.)
C) Calculate the covariance between advertising and sales. (Round your answer to 2 decimal places.)
D) Interpret the covariance between advertising and sales.
No correlation, positive correlation, or negative correlation?
E) Calculate the correlation coefficient between advertising and sales. (Round your answer to 2 decimal
places.)
F) Interpret the correlation coefficient between advertising and sales.
No correlation, strong negative correlation, weak positive correlation, strong positive correlation, or
weak negative correlation?
10. The scheduled arrival time for a daily flight from Boston to New York is 9:25 am. Historical data show
that the arrival time follows the continuous uniform distribution with an early arrival time of 9:16 am
and a late arrival time of 9:49 am.
A) After converting the time data to a minute scale, calculate the mean and the standard deviation for
the distribution. (Round your answers to 2 decimal places.)
B) What is the probability that a flight arrives late (later than 9:25 am)? (Do not round intermediate
calculations. Round your answer to 2 decimal places.)
11. Consider the following hypotheses:
H0: μ ≥ 210
HA: μ< 210
The population is normally distributed. A sample produces the following observations:
186
193
211
186
209
186
Use the critical value approach to conduct the test at a 5% level of significance. Use Table 2.
A) Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places.
Round your answers to 2 decimal places.)
B) Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round
intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
C) Calculate the critical value of the test statistic. (Negative value should be indicated by a minus sign.
Round intermediate calculations to 4 decimal places. Round your answer to 3 decimal places.)
D) What is the conclusion? Please select one of the following
D1) Do not reject H0 since the value of the test statistic is less than the negative critical value.
D2) Do not reject H0 since the value of the test statistic is not less than the negative critical value.
D3) Reject H0 since the value of the test statistic is less than the negative critical value.
D4) Reject H0 since the value of the test statistic is not less than the negative critical value.
12. A retailer is looking to evaluate its customer service. Management has determined that if the retailer
wants to stay competitive, then it will have to have at least a 86% satisfaction rate among its customers.
Management will take corrective actions if the satisfaction rate falls below 86%. A survey of 1,260
customers showed that 1,071 were satisfied with their customer service. Use Table 1.
A) Select the hypotheses to test if the retailer needs to improve its services. Please select one of the
following.
A1) H0: p ≤ 0.86; HA: p > 0.86
A2) H0: p = 0.86; HA: p ≠ 0.86
A3) H0: p ≥ 0.86; HA: p < 0.86
B) What is the value of the appropriate test statistic? (Negative value should be indicated by a minus
sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
C) Compute the p-value. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)
D) What is the conclusion?
The management WILL take correction action or management WILL NOT take correction action.
13. Which of the following variables is not continuous?
A) Time of a flight between Atlanta and Chicago
B) Average temperature in the month of July in Orlando
C) The number of obtained heads when a fair coin is tossed 20 times
D) Height of NBA players
14. In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a
random sample of 12 recent loans is taken. The average calculated from this sample is 5.30%. It can be
assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.3%.
Compute 95% and 99% confidence intervals for the population mean 30-year fixed mortgage rate. Use
Table 1. (Round intermediate calculations to 4 decimal places, "z" value and final answers to 2 decimal
places. Enter your answers as percentages, not decimals.)
Confidence Level
95%
99%
?
?
Confidence Interval
to
to
?
?
15. For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per
100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). The
regression results are shown.
ANOVA
df
Regression
Residual
2
26
SS
MS
F
3,536,461 1,768,230.5 11.08998
4,145,543 159,444.0
Significance
F
3.3E-04
Total
28
7,682,004
A) Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
B) What proportion of the variability in crime rate is explained by the variability in the explanatory
variables? (Round your answer to 4 decimal places.)
C) What proportion is unexplained? (Round your answer to 4 decimal places.)
16. At the end of a semester, college students evaluate their instructors by assigning them to one of the
following categories: Excellent, Good, Average, Below Average, and Poor. The measurement scale is a(n)
____________.
Ratio scale, ordinal scale, interval scale, or nominal scale?
17. Consider the following hypotheses
H0: μ ≥ 205
HA: μ< 205
A sample of 83 observations results in a sample mean of 202. The population standard deviation is
known to be 33. Use Table 1.
A) What is the critical value for the test with α = 0.10 and with α = 0.05? (Negative values should be
indicated by a minus sign. Round your answers to 2 decimal places.)
B) Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round
intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)
C) Does the above sample evidence enable us to reject the null hypothesis at α = 0.10? Please select
one of the following
C1) No since the value of the test statistic is not less than the negative critical value.
C2)Yes since the value of the test statistic is less than the negative critical value
C3)Yes since the value of the test statistic is not less than the negative critical value.
C4) No since the value of the test statistic is less than the negative critical value.
D) Does the above sample evidence enable us to reject the null hypothesis at α = 0.05? Please select
one of the following.
D1) No since the value of the test statistic is not less than the negative critical value.
D2)Yes since the value of the test statistic is less than the negative critical value.
D3)Yes since the value of the test statistic is not less than the negative critical value.
D4) No since the value of the test statistic is less than the negative critical value.
18. (Use computer) Assume that X is a hypergeometric random variable with N = 53, S = 21, and n = 13.
Calculate the following probabilities. (Round your answers to 4 decimal places.)
A)P(X = 6)= ?
B)P(X ≥ 2)= ?
C) P(X ≤ 5)= ?
19. The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of
2010 are reported in the following table. Use Table 2.
Months
January 2010
February 2010
March 2010
April 2010
May 2010
June 2010
Closing Stock Price
$5
6
9
8
10
4
A)
Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4
decimal places and "sample mean" and "sample standard deviation" to 2 decimal places.)
B) Compute the 90% confidence interval for the mean stock price of Panera Bread Co., assuming that
the stock price is normally distributed. (Round "t" value to 3 decimal places, and final answers to 2
decimal places.)
Confidence Level
?
to
?
C) What happens to the margin of error if a higher confidence level is used for the interval estimate?
The margin of error INCREASES or DECREASES as the confidence level increase.
20. A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The
management decides to evaluate the satisfaction surveys of its next 60 customers. The dealer will be
fined if the number of customers who report favorably is between 40 and 44. The dealership will be
dissolved if fewer than 40 report favorably. It is known that 72% of the dealer’s customers report
favorably on satisfaction surveys. Use Table 1.
A) What is the probability that the dealer will be fined? (Round intermediate calculations to 4 decimal
places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
B) What is the probability that the dealership will be dissolved? (Round intermediate calculations to 4
decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)
21. Consider the following sample data
x
y
16
41
29
40
14
40
32
37
10
37
25
48
15
35
15
44
A) Calculate b1 and b0. What is the sample regression equation? (Round intermediate calculations to 4
decimal places and final answers to 2 decimal places.)
y-hat =
?
₊
?
x
B) Find the predicted value for y if x equals 13, 18, and 23. (Round intermediate coefficient values and
final answers to 2 decimal places.)
If x = 13
If x = 18
If x - 23
y-hat
?
?
?
22. The time required to assemble an electronic component is normally distributed with a mean and a
standard deviation of 20 minutes and 14 minutes, respectively. Use Table 1.
A) Find the probability that a randomly picked assembly takes between 17 and 22 minutes. (Round "z"
value to 2 decimal places and final answer to 4 decimal places.)
B) It is unusual for the assembly time to be above 38 minutes or below 2 minutes. What proportion of
assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to
4 decimal places.)
23. The historical returns on a balanced portfolio have had an average return of 14% and a standard
deviation of 16%. Assume that returns on this portfolio follow a normal distribution. Use the empirical
rule for normal distributions to answer the following questions
A) What percentage of returns were greater than 30%? (Round your answer to 1 decimal place.)
B) What percentage of returns were below −18%? (Round your answer to 1 decimal place.)
24. India is the second most populous country in the world, with a population of over 1 billion people.
Although the government has offered various incentives for population control, some argue that the
birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the
following probability distribution of the household size in India.
Household Size
1
2
Probability
0.03
0.09
3
4
5
6
7
8
0.14
0.22
0.24
0.15
0.08
0.05
A) What is the probability that there are less than 5 members in a typical household in India? (Round
your answer to 2 decimal places.)
B) What is the probability that there are 5 or more members in a typical household in India? (Round
your answer to 2 decimal places.)
C) What is the probability that the number of members in a typical household in India is greater than 5
and less than 8 members? (Round your answer to 2 decimal places.)