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Nov. 2, 1995 Quant II Exam Questions and Answers, Exams of Business Statistics

Sam Higginbottom Institute of Agriculture, Technology and SciencesBusiness Statistics

Questions and answers from a quantitative methods exam held on november 2, 1995. The exam covers topics such as statistical analysis, regression analysis, and hypothesis testing.

Typology: Exams

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Uploaded on 02/26/2013

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Exam 2, Nov. 2, 1995, Quant II
The exam questions and answer sheet are both to be turned in to your Discussion Section instruc-
tor at the end of the exam. Be sure to code your Section number under OPTIONAL CODES
in positions L M N.
1. A class has asked their instructor to “grade on the curve.” With this system the instructor is
required to give preselected percentages of the various possible grades. In particular, the top
10% of the class must receive A’s. If exam scores are normally distributed with mean 82.0 and
standard deviation 2.34, what exam score corresponds to the lowest A grade?
A) 70
B) 75
C) 80
D) 85
E) 90
2. A scatterplot and least squares regression line are shown below for five data points. If the
point with coordinates (x,y)=(4,9) were changed to (x,y)=(4,6) what can we say about the new
fitted regression line?
A) the y-intercept would increase and the slope would increase
B) the y-intercept would decrease and the slope would increase
C) the y-intercept would increase and the slope would decrease
D) the y-intercept would decrease and the slope would decrease
E) None of the above.
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Download Nov. 2, 1995 Quant II Exam Questions and Answers and more Exams Business Statistics in PDF only on Docsity!

Exam 2, Nov. 2, 1995, Quant II

The exam questions and answer sheet are both to be turned in to your Discussion Section instruc- tor at the end of the exam. Be sure to code your Section number under OPTIONAL CODES in positions L M N.

  1. A class has asked their instructor to “grade on the curve.” With this system the instructor is required to give preselected percentages of the various possible grades. In particular, the top 10% of the class must receive A’s. If exam scores are normally distributed with mean 82.0 and standard deviation 2.34, what exam score corresponds to the lowest A grade? A) 70 B) 75 C) 80 D) 85 E) 90
  2. A scatterplot and least squares regression line are shown below for five data points. If the point with coordinates ( x , y )=(4,9) were changed to ( x , y )=(4,6) what can we say about the new fitted regression line?

A) the y -intercept would increase and the slope would increase B) the y -intercept would decrease and the slope would increase C) the y -intercept would increase and the slope would decrease D) the y -intercept would decrease and the slope would decrease E) None of the above.

0 1 2 3 4

10 9 8 7 6 x

y

Q

II

  1. Data design quality refers to assessment of whether the data collected are relevant to the problem we wish to solve. A) True B) False
  2. The least squares regression line is that line which makes the sum of squared vertical distances between the observation pairs and the fitted line as small as possible. A) True B) False
  3. A set of data pairs has the following summary statistics: = 10, = 50, s (^) x = 2, s (^) y = 3, and r = 0.5. What is the equation for the least squares regression line in original terms of x and y?

A) =0.5 x B) =0.75 x C) =45+0.5 x D) =42.5+0.75 x E) None of the above.

  1. What is the area under the standard normal curve between the z -scores of −1.3 and +0.91?

A) 0. B) 0. C) 0. D) 0. E) None of the above.

  1. Twenty-five data pairs are under consideration. The first pair is x = 2 with y = 6. What is the

fitted value for this data pair for the quadratic regression curve with equation = 1 + x^2? A) 1 B) 2 C) 5 D) 6 E) None of the above.

x y

y ˆ y ˆ y ˆ y ˆ

y ˆ

  1. A factorial experiment has two factors. The first factor has three levels and the second factor has two levels. If the experiment has three replications, how many observations will be recorded? A) 2 B) 3 C) 6 D) 12 E) 18
  2. An elevator carries 9 people in a load. The weights of people vary according to many factors but may be described by a distribution with mean 150 pounds and standard deviation 30 pounds. Over many loads each of 9 people, about what percentage of loads will exceed the safe load limit of 1700 pounds? A) 0.01% B) 0.1% C) 1% D) 5% E) None of the above.
  3. In general, the larger the value of the adjusted R^2 , the better the regression model.

A) True B) False

  1. Hawkeye Supply Inc. has randomly selected 100 steel bolts from a large shipment. Suppose that the individual bolt lengths in the shipment may be described by a distribution with mean 3 inches and standard deviation 0.1 inches. Let y denote the average bolt length for the sample of 100 bolts. If the sampling were repeated many times, what fraction of the averages, y , would be larger than 2.98 inches? A) 0. B) 0. C) 0. D) 0. E) None of the above.
  2. Is the following expression true or false for a multiple regression model? Residual = Observed Response − Fitted Value A) True B) False
  1. What is the 75 th^ percentile of a normal distribution with mean 65 and standard deviation 7.463? A) 67 B) 68 C) 69 D) 70 E) 91
  2. Twenty data pairs are under consideration. The second pair has x = 2 with y = 3. What is the

value of the residual for this data pair for the line with equation = 1 + x? A) 0 B) 1 C) 2 D) 3 E) 4

  1. Alligators have weights that are distributed approximately according to a normal distribution with mean 150 kilograms and standard deviation 56 kilograms. Only alligators that weigh at least 200 kilograms may be legally caught. What percentage of all alligators may be legally caught? (to the nearest whole percent ) A) 11% B) 19% C) 81% D) 89% E) None of the above.
  2. Stanford-Binet IQ scores are approximately normally distributed with a mean of 100. If the 84th percentile of the scores is 116, what is the standard deviation of the scores? A) 1 B) 16 C) 84 D) 100 E) 116
  3. In multiple regression modeling, residual plots that are random indicate that the model can be improved. A) True B) False

y ˆ

  1. The table below shows four data pairs together with some partial results on fitted values and residuals for two possible models—one linear and one quadratic. These models were not necessarily found using least squares.

Which curve fits the data better in the sense of least squares? A) Curve I fits better since its residuals add to zero. B) Curve I fits better since its sum of squared residuals is smaller than for Curve II. C) Curve I fits better since it is the least squares regression line for these data. D) Curve II fits better since its sum of squared residuals is smaller than for Curve I. E) Curve II fits better since two of its residuals are zero.

  1. A standard deviation control chart displays the changes in variation within subgroups over time. A) True B) False
  2. In a normal probablility plot, the closer the plot is to some straight line, the more support we have for a normal distribution for the data. A) True B) False
  3. Common causes of variation in a measured variable that are due to chance and remain in the system unless the process is fundamentally altered. A) True B) False
  4. Suppose that a change in supplier of raw materials has the effect of increasing variability of a measured variable but not its mean level. Which of the following statements is true? A) A mean chart will detect the change but a standard deviation chart will be unaffected. B) A standard deviation chart will detect the change but a mean chart will be unaffected. C) Both mean charts and standard deviations charts will detect the change. D) No control chart can be expected to effectively deal with this situation. E) None of the above.

Data Curve I Curve^ II

y x (^) x^2 FITTED RESIDUAL FITTED RESIDUAL 1 1 1 0.7 0.3 0.75 0. 1 2 4 1.4 −0.4 0. 2 3 9 2.1 −0.1 1.75 0. 3 4 16 2.8 0.2 3.00 0.

y ˆ^ = 0.7 x y ˆ (^) = 1 – 0.5 x +0.25 x^2

  1. A portion of an ANOVA (analysis-of-variance) table from a multiple regression calculation is shown below. What is the value of s (the residual standard deviation) for this regression?

A) 4.

B) 8.

C) 21.

D) 70.

E) None of the above.

  1. Referring to the ANOVA table in problem 33, what is the value of R^2 for this regression?

A) 0.80% B) 19.95% C) 70.01% D) 80.05% E) None of the above.

Source SS df Regression 510.90 3 Error 127.33 6 Total