STAT125-HK. BUSINESS STATISTICS (STAT125-HK) > TAKE ASSESSMENT: MIDTERM EXAM

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1The probability that house sales will increase in the next 6 months is estimated to be 0.25. Theprobability that the interest rates on housing loans will go up in the same period is estimated tobe 0.74. The probability that house sales or interest rates will go up during the next 6 months isestimated to be 0.89. The probability that house sales will increase but interest rates will notduring the next 6 months is:a. 0.065b. 0.15c. 0.51d. 0.89Question

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2The process of using sample statistics to draw conclusions about true population parameters iscalleda. statistical inference.b. the scientific method.c. sampling.d. descriptive statistics.Question

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3Which of the following is NOT a reason for obtaining data?a. Data are needed to formulate a statistical model.b. Data are needed to evaluate conformance to standards.c. Data are needed to measure performance of an ongoing production process.d. Data are needed to provide input to a study.Question

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4A catalog company that receives the majority of its orders by telephone conducted a study todetermine how long customers were willing to wait on hold before ordering a product. Thelength of time was found to be a random variable best approximated by an exponentialdistribution with a mean equal to 3 minutes. What proportion of customers having to hold morethan 1.5 minutes will hang up before placing an order?a. 0.86466b. 0.60653

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c. 0.39347d. 0.13534Question

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5Selection of raffle tickets from a large bowl is an example ofa. sampling with replacement.b. sampling without replacement.c. subjective probability.d. None of the above.Question6The width of each bar in a histogram corresponds to thea. differences between the boundaries of the class.b. number of observations in each class.c. midpoint of each class.d. percentage of observations in each class.Question7If two events are mutually exclusive and collectively exhaustive, what is the probability that oneor the other occurs?a. 0.b. 0.50.c. 1.00.d. Cannot be determined from the information given.Question

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8Which of the following is not an element of descriptive statistical problems?a. An inference made about the population based on the sample.b. The population or sample of interest.c. Tables, graphs, or numerical summary tools.d. Identification of patterns in the data.Question9Which of the following statistics is not a measure of central tendency?a. Mean.

b. Median.c. Mode.d. Q3.Question

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10Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 millionin 1994. Suppose a sample of 100 major league players was taken. Find the approximateprobability that the average salary of the 100 players exceeded $1 million.a. Approximately 0b. 0.2357c. 0.7357d. Approximately 1Question 11

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If two equally likely events A and B are mutually exclusive and collectively exhaustive, what isthe probability that event A occurs?a. 0.b. 0.50.c. 1.00.d. Cannot be determined from the information given.Question

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12TABLE 2-6A sample of 200 students at a Big-Ten university was taken after the midterm to ask themwhether they went bar hopping the weekend before the midterm or spent the weekendstudying, and whether they did well or poorly on the midterm. The following table contains theresult.Did Well on Midterm Did Poorly on MidtermStudying for Exam 80

20

Went Bar Hopping 30

70

Referring to Table 2-6, of those who did well on the midterm in the sample, _______ percent ofthem went bar hopping the weekend before the midterm.a. 15b. 27.27c. 30d. 50

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13TABLE 2-5The following are the durations in minutes of a sample of long-distance phone calls madewithin the continental United States reported by one long-distance carrier.Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15 0.1515 but less than 20 0.1020 but less than 25 0.0725 but less than 30 0.0730 or more

0.02

Referring to Table 2-5, what is the width of each class?a. 1 minuteb. 5 minutesc. 2%d. 100%Question

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14According to a survey of American households, the probability that the residents own 2 cars ifannual household income is over $25,000 is 80%. Of the households surveyed, 60% hadincomes over $25,000 and 70% had 2 cars. The probability that annual household income isover $25,000 if the residents of a household do not own 2 cars is:a. 0.12b. 0.18c. 0.40d. 0.55Question

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15A study is under way in Yosemite National Forest to determine the adult height of Americanpine trees. Specifically, the study is attempting to determine what factors aid a tree in reachingheights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult Americanpines. The study involves collecting heights from 250 randomly selected adult American pinetrees and analyzing the results. Identify the population from which the study was sampled.

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a. The 250 randomly selected adult American pine trees.b. The 25,000 adult American pine trees in the forest.c. All the adult American pine trees taller than 60 feet.d. All American pine trees, of any age, in the forest.Question

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16When extreme values are present in a set of data, which of the following descriptive summarymeasures are most appropriate?a. CV and range.b. mean and standard deviation.c. interquartile range and median.d. variance and interquartile range.Question

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17A population frame for a survey contains a listing of 72,345 names. Using a table of randomnumbers, how many digits will the code numbers for each member of your population contain?a. 3b. 4c. 5d. 6Question

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18A recent survey of banks revealed the following distribution for the interest rate being chargedon a home loan (based on a 30-year mortgage with a 10% down payment).Interest Rate: 7.0% 7.5% 8.0% 8.5% >8.5%Probability

0.12 0.23 0.24 0.35 0.06

If a bank is selected at random from this distribution, what is the chance that the interest ratecharged on a home loan will exceed 8.0%?a. 0.06b. 0.41c. 0.59d. 1.00Question

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19Referring to the histogram from Table 2-3, how many graduating seniors attended theluncheon?

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a. 4b. 152c. 275d. 388Question

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20TABLE 2-4A survey was conducted to determine how people rated the quality of programming availableon television. Respondents were asked to rate the overall quality from 0 (no quality at all) to100 (extremely good quality). The stem-and-leaf display of the data is shown below.Stem Leaves3

24

4

03478999

5

0112345

6

12566

7

01

89

2

Referring to Table 2-4, what percentage of the respondents rated overall television quality witha rating between 50 and 75?a. 0.11b. 0.40c. 0.44d. 0.56Question

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21The Central Limit Theorem is important in statistics becausea. for a large n, it says the population is approximately normal.b. for any population, it says the sampling distribution of the sample mean isapproximately normal, regardless of the sample size.c. for a large n, it says the sampling distribution of the sample mean is approximatelynormal, regardless of the shape of the population.

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d. for any sized sample, it says the sampling distribution of the sample mean isapproximately normal.Question

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22If you were constructing a 99% confidence interval of the population mean based on a sampleof n = 25 where the standard deviation of the sample s = 0.05, the critical value of t will bea. 2.7969b. 2.7874c. 2.4922d. 2.4851Question

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23A statistics student found a reference in the campus library that contained the median familyincomes for all 50 states. She would report her data as being collected usinga. a designed experiment.b. observational data.c. a random sample.d. a published source.Question

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24TABLE 2-5The following are the durations in minutes of a sample of long-distance phone calls madewithin the continental United States reported by one long-distance carrier.Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15 0.1515 but less than 20 0.1020 but less than 25 0.0725 but less than 30 0.0730 or more

0.02

Referring to Table 2-5, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5minutes?a. 10b. 185

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c. 295d. 500Question

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25The employees of a company were surveyed on questions regarding their educationalbackground and marital status. Of the 600 employees, 400 had college degrees, 100 weresingle, and 60 were single college graduates. The probability that an employee of thecompany is single or has a college degree is:a. 0.10b. 0.25c. 0.667d. 0.733Question

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26The probability that house sales will increase in the next 6 months is estimated to be 0.25. Theprobability that the interest rates on housing loans will go up in the same period is estimated tobe 0.74. The probability that house sales or interest rates will go up during the next 6 monthsis estimated to be 0.89. The probability that neither house sales nor interest rates will increaseduring the next 6 months is:a. 0.11b. 0.195c. 0.89d. 0.90Question

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27A confidence interval was used to estimate the proportion of statistics students that arefemales. A random sample of 72 statistics students generated the following 90% confidenceinterval: (0.438, 0.642). Based on the interval above, is the population proportion of femalesequal to 0.60?a. No, and we are 90% sure of it.b. No. The proportion is 54.17%.c. Maybe. 0.60 is a believable value of the population proportion based on theinformation above.d. Yes, and we are 90% sure of it.Question

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28Since a _______ is not a randomly selected probability sample, there is no way to know howwell it represents the overall population.

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a. simple random sampleb. quota samplec. stratified sampled. cluster sampleQuestion

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29TABLE 2-6A sample of 200 students at a Big-Ten university was taken after the midterm to ask themwhether they went bar hopping the weekend before the midterm or spent the weekendstudying, and whether they did well or poorly on the midterm. The following table contains theresult.Did Well on Midterm Did Poorly on MidtermStudying for Exam 80

20

Went Bar Hopping 30

70

Referring to Table 2-6, _______ percent of the students in the sample went bar hopping theweekend before the midterm and did well on the midterm.a. 15b. 27.27c. 30d. 50Question

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30The collection of all possible events is calleda. a simple probability.b. a sample space.c. a joint probability.d. the null set.Question31A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the labconducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 perweek. Interpret this value.a. Most of the weeks resulted in rat costs of $13.00.b. The median cost for the distribution of rat costs is $13.00.

c. The expected or average cost for all weekly rat purchases is $13.00.d. The rat cost that occurs more often than any other is $13.00.Question

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32Which of the following is not true about the Student’s t distribution?a. It has more area in the tails and less in the center than does the normal distribution.b. It is used to construct confidence intervals for the population mean when thepopulation standard deviation is known.c. It is bell shaped and symmetrical.d. As the number of degrees of freedom increases, the t distribution approaches thenormal distribution.Question

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33If two events are mutually exclusive, what is the probability that one or the other occurs?a. 0.b. 0.50.c. 1.00.d. Cannot be determined from the information given.Question

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34Tim was planning for a meeting with his boss to discuss a raise in his annual salary. Inpreparation, he wanted to use the Consumer Price Index to determine the percentageincrease in his salary in terms of real income over the last three years. Which of the 4 methodsof data collection was involved when he used the Consumer Price Index?a. Published sourcesb. Experimentationc. Surveyingd. ObservationQuestion

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35A professor of economics at a small Texas university wanted to determine what year in schoolstudents were taking his tough economics course. Shown below is a pie chart of the results.What percentage of the class took the course prior to reaching their senior year?

a. 14%

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b. 44%c. 54%d. 86%Question

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36TABLE 2-5The following are the durations in minutes of a sample of long-distance phone calls madewithin the continental United States reported by one long-distance carrier.Time (in Minutes)

Relative Frequency

0 but less than 5

0.37

5 but less than 10

0.22

10 but less than 15 0.1515 but less than 20 0.1020 but less than 25 0.0725 but less than 30 0.0730 or more

0.02

Referring to Table 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutesor longer?a. 10b. 14c. 26d. 74Question

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37The chancellor of a major university was concerned about alcohol abuse on her campus andwanted to find out the portion of students at her university who visited campus bars everyweekend. Her advisor took a random sample of 250 students. The portion of students in thesample who visited campus bars every weekend is an example of __________.a. a categorical random variable.b. a discrete random variable.c. a parameter.d. a statistic.Question

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38Which of the following statements about the median is not true?

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a. It is more affected by extreme values than the mean.b. It is a measure of central tendency.c. It is equal to Q2.d. It is equal to the mode in bell-shaped "normal" distributions.Question

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39Most analysts focus on the cost of tuition as the way to measure the cost of a collegeeducation. But incidentals, such as textbook costs, are rarely considered. A researcher atDrummand University wishes to estimate the textbook costs of first-year students atDrummand. To do so, she monitored the textbook cost of 250 first-year students and foundthat their average textbook cost was $300 per semester. Identify the sample in the study.a. All Drummand University students.b. All college students.c. All first-year Drummand University students.d. The 250 students that were monitored.Question

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40The head librarian at the Library of Congress has asked her assistant for an interval estimateof the mean number of books checked out each day. The assistant provides the followinginterval estimate: from 740 to 920 books per day. If the head librarian knows that thepopulation standard deviation is 150 books checked out per day, and she asked her assistantto use 25 days of data to construct the interval estimate, what confidence level can she attachto the interval estimate?a. 99.7%b. 99.0%c. 98.0%d. 95.4%Question

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41Which of the following is true regarding the sampling distribution of the mean for a largesample size?a. It has the same shape, mean, and standard deviation as the population.b. It has a normal distribution with the same mean and standard deviation as thepopulation.c. It has the same shape and mean as the population, but has a smaller standarddeviation.d. It has a normal distribution with the same mean as the population but with a smallerstandard deviation.

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42A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the labconducts. Prices for 100 rats follow the following distribution:Price:

$10.00 $12.50 $15.00

Probability: 0.35

0.40

0.25

How much should the lab budget for next year’s rat orders be, assuming this distribution doesnot change?a. $520b. $637c. $650d. $780Question

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43The portfolio expected return of two investmentsa. will be higher when the covariance is zero.b. will be higher when the covariance is negative.c. will be higher when the covariance is positive.d. does not depend on the covariance.Question44According to a survey of American households, the probability that the residents own 2 cars ifannual household income is over $25,000 is 80%. Of the households surveyed, 60% hadincomes over $25,000 and 70% had 2 cars. The probability that the residents of a householddo not own 2 cars and have an income over $25,000 a year is:a. 0.12b. 0.18c. 0.22d. 0.48Question

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45Which of the following is most likely a parameter as opposed to a statistic?a. The average score of the first five students completing an assignment.b. The proportion of females registered to vote in a county.c. The average height of people randomly selected from a database.d. The proportion of trucks stopped yesterday that were cited for bad brakes.

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46Which of the mean, median, mode, and geometric mean are resistant measures of centraltendency?a. The mean and median only.b. The median and mode only.c. The mode and geometric mean only.d. The mean and mode only.Question

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47The collection and summarization of the socioeconomic and physical characteristics of theemployees of a particular firm is an example ofa. inferential statistics.b. descriptive statistics.c. a parameter.d. a statistic.Question

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48A population frame for a survey contains a listing of 6,179 names. Using a table of randomnumbers, which of the following code numbers will appear on your list?a. 06b. 0694c. 6946d. 61790Question

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49In left-skewed distributions, which of the following is the correct statement?a. The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.b. The distance from the smallest observation to Q1 is larger than the distance fromQ3 to the largest observation.c. The distance from the smallest observation to Q2 is smaller than the distance fromQ2 to the largest observation.d. The distance from Q1 to Q3 is twice the distance from Q1 to Q2.Question

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50Why is the Central Limit Theorem so important to the study of sampling distributions?

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a. It allows us to disregard the size of the sample selected when the population is notnormal.b. It allows us to disregard the shape of the sampling distribution when the size of thepopulation is large.c. It allows us to disregard the size of the population we are sampling from.d. It allows us to disregard the shape of the population when n is large.STAT125-HK. BUSINESS STATISTICS (STAT125-HK) > TAKE ASSESSMENT: FINAL EXAM

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1In testing for differences between the means of 2 independent populations, the null hypothesisis:a. H0: μ1 – μ2 = 2.b. H0: μ1 – μ2 = 0.c. H0: μ1 – μ2 > 0.d. H0: μ1 – μ2 < 2.Question

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2A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.To test this claim against the alternative that the actual proportion of doctors who recommendaspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that theyrecommend aspirin. The value of the test statistic in this problem is approximately equal to:a. -4.12b. -2.33c. -1.86d. -0.07Question

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3If a group of independent variables are not significant individually but are significant as a groupat a specified level of significance, this is most likely due toa. autocorrelation.b. the presence of dummy variables.c. the absence of dummy variables.d. collinearity.Question

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4TABLE 13-2

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A candy bar manufacturer is interested in trying to estimate how sales are influenced by theprice of their product. To do this, the company randomly chooses 6 small cities and offers thecandy bar at different prices. Using candy bar sales as the dependent variable, the companywill conduct a simple linear regression on the data below:City

Price

Sales

($)River

1.30

100

1.60

90

Ellsworth 1.80

90

Prescott 2.00

40

Rock Elm 2.40

38

Stillwater 2.90

32

FallsHudson

Referring to Table 13-2, what is the coefficient of correlation for these data?a. -0.8854b. -0.7839c. 0.7839d. 0.8854Question

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5The Y-intercept (b0) represents thea. predicted value of Y when X = 0.b. change in estimated average Y per unit change in X.c. predicted value of Y.d. variation around the sample regression line.Question6TABLE 14-5A microeconomist wants to determine how corporate sales are influenced by capital and wagespending by companies. She proceeds to randomly select 26 large corporations and recordinformation in millions of dollars. The Microsoft Excel output below shows results of this μltipleregression.SUMMARY OUTPUTRegression Statistics

Multiple R

0.830

R Square

0.689

Adjusted R

0.662

SquareStandard

17501.643

ErrorObservations 26ANOVA

df SS

MS

F

Signif F

Regression 2 15579777040 7789888520 25.432 0.0001Residual

23 7045072780 306307512

Total

25 22624849820Coeff

StdError

t Stat P-value

Intercept 15800.0000 6038.2999 2.617 0.0154Capital

0.1245

0.2045

0.609 0.5485

Wages

7.0762

1.4729

4.804 0.0001

Referring to Table 14-5, what are the predicted sales (in millions of dollars) for a companyspending $100 million on capital and $100 million on wages?a. 15,800.00b. 16,520.07c. 17,277.49d. 20,455.98Question

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7If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift ofthe mean to 105 will be ________ the probability of detecting a shift of the mean to 110.a. less thanb. greater thanc. equal tod. not comparable toQuestion

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8TABLE 11-1Psychologists have found that people are generally reluctant to transmit bad news to theirpeers. This phenomenon has been termed the "ΜM effect." To investigate the cause of the ΜMeffect, 40 undergraduates at Duke University participated in an experiment. Each subject wasasked to administer an IQ test to another student and then provide the test taker with his or her

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percentile score. Unknown to the subject, the test taker was a bogus student who was workingwith the researchers. The experimenters manipulated two factors: subject visibility andsuccess of test taker, each at two levels. Subject visibility was either visible or not visible tothe test taker. Success of the test taker was either visible or not visible to the test taker.Success of the test taker was either top 20% or bottom 20%. Ten subjects were randomlyassigned to each of the 2 x 2 = 4 experimental conditions, then the time (in seconds) betweenthe end of the test and the delivery of the percentile score from the subject to the test taker wasmeasured. (This variable is called the latency to feedback.) The data were subjected toappropriate analyses with the following results.Source

df SS

MS

F

PR >F

Subject

1 1380.24

1380.24 4.26 0.043

Test taker 1 1325.16

1325.16 4.09 0.050

visibility

successInteraction 1 3385.80

3385.80 10.45 0.002

Error

36 11,664.00 324.00

Total

39 17,755.20

Referring to Table 11-1, in the context of this study, interpret the statement: "Subject visibilityand test taker success interact."a. The difference between the mean feedback time for visible and nonvisible subjectsdepends on the success of the test taker.b. The difference between the mean feedback time for test takers scoring in the top 20%and bottom 20% depends on the visibility of the subject.c. The relationship between feedback time and subject visibility depends on the successof the test taker.d. All of the above are correct interpretations.Question

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9TABLE 13-1A large national bank charges local companies for using their services. A bank official reportedthe results of a regression analysis designed to predict the bank’s charges (Y) — measured indollars per month — for services rendered to local companies. One independent variable usedto predict service charge to a company is the company’s sales revenue (X) — measured inmillions of dollars. Data for 21 companies who use the bank’s services were used to fit themodel:

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E(Y) = β0 + β1XThe results of the simple linear regression are provided below.Y = -2,700+20X, syx = 65, two-tailed p value = 0.034 (for testing β1)Referring to Table 13-1, interpret the p…