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Quantitative II Exam, March 29, 1995, Exams of Business Statistics

Senate of Serampore College (University)Business Statistics

A set of exam questions and answer sheet for quantitative ii course, held on march 29, 1995. The exam covers various topics such as correlation coefficient, regression analysis, residual plots, normal distribution, and hypothesis testing. The exam includes multiple-choice questions, true/false questions, and problems requiring calculations.

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1
Exam 2, Mar. 29, 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. Please mark all of your answers on the answer sheet using a #2 pencil.
Code your name, ID number, and Section number on the answer sheet.
1. If an experimental treatment is deemed to have harmful side effects, it is called a placebo.
A) True B) False
2. If data have a very strong upward but curved relationship, it is possible to get a correlation
coefficient that is larger than +1.
A) True B) False
3. In a factorial experiment all treatments combinations are run in one replication.
A) True B) False
4. 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
lowest 10% of the class must receive F’s. If exam scores are normally distributed with mean
83.0 and standard deviation 2.34, what exam score corresponds to the highest F grade?
A) 50
B) 60
C) 70
D) 78
E) 80
5. Correlations based on pairs of averages or totals of smaller units of study are usually larger in
magnitude than if they were based on individual measurements.
A) True B) False
6. Autocorrelation documents the correlation of a time series with its own past history.
A) True B) False
7. In general, the larger the residual standard deviation, the better the regression model.
A) True B) False
8. In multiple regression modeling, the most basic residual plot is the plot of residuals versus the
corresponding fitted values.
A) True B) False
Q
II
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Download Quantitative II Exam, March 29, 1995 and more Exams Business Statistics in PDF only on Docsity!

Exam 2, Mar. 29, 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. Please mark all of your answers on the answer sheet using a #2 pencil. Code your name, ID number, and Section number on the answer sheet.

  1. If an experimental treatment is deemed to have harmful side effects, it is called a placebo.

A) True B) False

  1. If data have a very strong upward but curved relationship, it is possible to get a correlation coefficient that is larger than +1. A) True B) False
  2. In a factorial experiment all treatments combinations are run in one replication.

A) True B) False

  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 lowest 10% of the class must receive F’s. If exam scores are normally distributed with mean 83.0 and standard deviation 2.34, what exam score corresponds to the highest F grade? A) 50 B) 60 C) 70 D) 78 E) 80
  2. Correlations based on pairs of averages or totals of smaller units of study are usually larger in magnitude than if they were based on individual measurements. A) True B) False
  3. Autocorrelation documents the correlation of a time series with its own past history.

A) True B) False

  1. In general, the larger the residual standard deviation, the better the regression model.

A) True B) False

  1. In multiple regression modeling, the most basic residual plot is the plot of residuals versus the corresponding fitted values. A) True B) False

Q

II

  1. A straight-line has been fit to model the relationship between Salary and Experience for 20 people. The residual plot is shown below. Points plotted for males use M as a plotting symbol. Females are plotted with an F.

Which of the following statements best describes this plot? A) The randomness shown in the plot indicates a good model. B) The plot shows that normality is a reasonable assumption. C) The plot shows that a quadratic model should be considered. D) The plot shows that least squares is an excellent criterion for fitting the line. E) The plot indicates that a parallel-lines model would explain the relationship better.

  1. We have 17 pairs of x-y data and are fitting a quadratic regression curve by least squares. How many degrees of freedom do the residuals have? A) 14 B) 15 C) 16 D) 32 E) 33
  2. A time series consists of the values 5, 9, 7, 4, 5 in that order. What is the value of the lag 1 autocorrelation coefficient? A) 0 B) 0. C) 0. D) 0. E) 0.
  1. The following table shows the responses of ten students to questions about their gender and the difficulty of an exam.

What percent of students thought the exam was easy? A) 10% B) 20% C) 30% D) 40% E) 50%

  1. Referring to the table in question 18: What percent of females thought the exam was hard?

A) 20% B) 40% C) 60% D) 80% E) 100%

  1. Referring to the table in question 18: What percent of those who thought the exam was easy were males? A) 50% B) 60% C) 65% D) 70% E) 75%

Student ID (^) Gender†

† 1 = female, 0 = male

Difficulty ‡

‡ 1 = easy, 2 = moderate, 3 = hard

Student ID Gender Difficulty 1 0 2 6 0 2 2 1 3 7 0 1 3 1 1 8 1 3 4 1 2 9 0 1 5 0 1 10 1 2

  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 one of its residuals is zero.

  1. Each year the General Social Survey, GSS, selects 1500 households throughout the U.S. using complicated randomization methods. People in the selected households are interviewed extensively to gather social science data. Such a study is best classified as A) a designed experiment with blinding of the subjects B) an observational study C) a designed study D) a double blind, designed experiment E) a designed experiment with neither blinding nor double blinding
  2. A factorial experiment has two factors. The first factor has two levels and the second factor has three levels. If the experiment is replicated twice, how many observations will be recorded? A) 2 B) 3 C) 5 D) 6 E) 12

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 3.

yˆ^ = 0.7x yˆ^ = 1 – 0.5x+0.25x 2

  1. The table below displays counts of people by gender and marital status.

What percent of the married people are female? (Round to the nearest whole percent.) A) 17% B) 33% C) 45% D) 50% E) 60%

  1. Referring to the table in Question 29, what percent of the people are single? (Round to the nearest whole percent.) A) 17% B) 33% C) 45% D) 60% E) 67%
  2. Consider normal scores calculated for a sample of 28 highly skewed observations. An analyst (mistakenly?) displays a stem-and-leaf diagram for the 28 normal scores values. Which one of the following describes a correct reaction to the shape of the stem-and-leaf diagram? A) The analyst is not surprised that the stem-and-leaf diagram shows the skewness in the data. B) The analyst is surprised that the stem-and-leaf diagram shows the skewness in the data. C) The analyst is not surprised that the stem-and-leaf diagram looks very normal. D) The analyst is surprised that the stem-and-leaf diagram looks very normal. E) The analyst is surprised that normal scores can be calculated for skewed data.

Gender

Marital Status Single Married Other female 200 50 50 male 100 60 40

  1. A truck carries 40 standard-sized containers in a load. The weights of the containers vary according to many factors but may be described by a distribution with mean 230 pounds and standard deviation 40.8 pounds. Over many loads, what percent of loads will exceed the legal load limit of 10,000 pounds? A) 1% B) 5% C) 10% D) 20% E) None of the above.
  2. The times necessary to complete service for a class of bank customers is described by a normal distribution with mean 15 minutes and standard deviation 2.1 minutes. Service times are considered excessive if they exceed 20 minutes. Over the long run, what percent of customers will experience excessive service times? A) 0.87% B) 2.38% C) 97.62% D) 99.13% E) None of the above.
  3. Hawkeye Supply Company has randomly selected 100 steel bolts from a large shipment. Suppose that the 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 less than 2.98 inches? A) 0. B) 0. C) 0. D) 0. E) None of the above.
  4. What is the 90 th^ percentile of a normal distribution with mean 75 and standard deviation 8.6?

A) 1. B) 10 C) 86 D) 90 E) 92

  1. The sequence plot of a time series of 48 monthly values is shown below. The lag 1 autocorrelation coefficient for this series is best described as: (Hint: What would the plot of the series versus the lag 1 of the series look like?)

A) Strongly negative B) Moderately negative C) Near zero D) Moderately positive E) Strongly positive

  1. The normal probability plot for the Iowa city sizes data is shown below.

This plot shows that: A) normality is strongly supported. B) normality is not^ supported since the curvature in the plot indicates that the distribution is skewed towards the high values. C) normality is not supported since the curvature in the plot indicates that the distribution is skewed towards the low values. D) normal scores plots cannot be used with skewed data. E) None of the above.