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Exam 2: Nov. 6, 1997, Quant II Form A
The 36 exam questions and answer sheet are both to be turned in to your Discussion Section instructor at the end of the exam. Code your name and ID number on the answer sheet. Code your Section number under OPTIONAL CODES in positions L M N. Please notice the Defective Question report, the Normal Distribution table, and the Formula Sheet at the end of the exam.
- A student collects some data on college students. For 100 students, he obtains two variables: College GPA and Average Weekly Hours Watching Television. He finds the correlation coefficient between the two variables to be +0.95. We can therefore conclude that watching television must cause students to get better grades. A) True B) False
- A basketball coach has an idea that training in ballet might help her players jump higher. To test this idea she divides her team randomly into two equal groups. One group is required to take six weeks of ballet training before the basketball season begins. The other group receives no ballet training. This study would be classified as A) a probability survey B) an observational study C) an experiment D) an observational survey E) None of the above.
- Consider the scatterplot of two variables shown at the right. From this plot, which of the following is the most reasonable estimate of the correlation coefficient between the two variables? A) −1. B) −0. C) +0. D) +0. E) +1.
- If a sequence of longitudinal data is random we expect the lag one autocorrelation coefficient to be near zero. A) True B) False
10 15 20 25
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5 X variable
Y variable
- Twenty pairs of data produced a least squares regression line with equation
The boss prefers simplicity so she wants to use the line with equation
Which one of the following statements is true? A) Line 1 will have a smaller value for the residual standard deviation. B) Line 2 will have a smaller value for the residual standard deviation. C) Line 1 will have a larger value for the total sum of squares. D) Line 2 will have a larger value the total sum of squares. E) Without having the data we cannot say which line will have smaller residual standard deviation nor larger total sum of squares.
- What can we say about the correlation coefficient for the data at the right? ( Do not calculate! ) A) It is −1. B) It is strongly negative. C) It is near zero. D) It is strongly positive. E) It is +1.
- A placebo is
A) a dummy treatment B) the control group C) the experimental group D) an aspirin treatment E) the treatment the researcher hopes will prove effective.
- Researchers have observed that drinking red wine, x , seems to lead to fewer men having heart attacks, y. More recently, others have noted that drinking red wine leads to headaches and people with headaches tend to take aspirin. Furthermore, aspirin is known to reduce the chances of having heart attacks. Given these facts, the relationship between x and y would be best described as being due to A) cause-and-effect B) mechanism C) consistency D) strong correlation E) a lurking variable
y ˆ^ = 0.0263 +0.547 x Line 1
y ˆ^ = 0.03 +0.5 x Line 2
x 2.02 2.95 4.89 3.21 3. y 4.11 2.10 1.21 2.98 2.
- Your friend tosses a pair of dice where one die is red and the other is green. She reports to you that she got a 6 total. Given this information, what is the chance that she rolled a 1 on the green die? A) 1/ B) 2/ C) 3/ D) 1/ E) 2/
- A set of data pairs has the following summary statistics: x = 40, y = 100, s (^) x = 3, s (^) y = 12, 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) =2 x C) =20 + 2 x D) =100 + 0.5 x E) None of the above.
- An interested company worker wants to model the relationship between years of job experience and salary. She uses least-squares to obtain the following fitted equation, where y is the annual salary (in dollars) and x is the number of years of experience: y = 20,000 + 2,500 x. Sarah, an economist for the company, has 14 years experience and is making $54, a year. What is the residual associated with Sarah? A) −2, B) −1, C) +1, D) +2, E) +2,
- The table at the right gives the joint distribution of two variables x and y. What is the expected value of y? A) 1/ B) 1/ C) 1 D) 2 E) None of the above.
y ˆ y ˆ y ˆ y ˆ
y^^1 1/4^ 1/4^0 0 0 1/4 1/ 0 1 2 x
- Suppose you are given the following least-squares regression equation, where y is the final exam score in a Spanish class, x 1 is the midterm exam score and x 2 is the gender of the student (0 = male, 1 = female): y = 0.83 + 1.01 x 1 − 3.63 x 2. What is the predicted final exam score (rounded to the nearest whole point) for a male student who got a 75 on the midterm exam? A) 73 B) 74 C) 75 D) 77 E) Cannot determine from the information given.
- you are conducting an experiment on popcorn. The factors of the experiment are Brand and Popper type. You have selected three brands of popcorn and two types of popper. You will measure how many cups of popped popcorn are produced. If you perform two replications of the experiment, how many total batches of popcorn will you have to make? A) 2 B) 3 C) 6 D) 7 E) 12
- In the Physician’s Health Study, a coin was flipped to decide which doctors took the aspirin and which took the placebo. Using the coin flip to decided which subjects get which treatment is an example of: A) randomization B) replication C) blinding D) stratification E) placebo
- Two variables x^ and y^ have an approximate straight-line relationship between them with a correlation coefficient of 0.7. If x were to increase by amount s (^) x how much would we predict that y would increase? A) s (^) x B) s (^) y C) 0.7 s (^) x D) 0.7 s (^) y E) 0.7 s^ y/s^ x
- The table below gives the breakdown of shoe sale transactions over a long period for a large shoe chain. An auditor selects one transaction at random from all of the transactions.
What is the chance that a Cash transaction is selected? A) 20% B) 35% C) 55% D) 80% E) None of the above.
- Refer to the previous problem. Given that a Credit Card transaction is selected, what is the chance that it is a Reebok transaction? A) 20% B) 30% C) 40% D) 50% E) None of the above.
- The table at the right gives the joint distribution of two variables x and y. What is the covariance between x and y? A) −1/ B) −1/ C) 0 D) 1/ E) 1/
- In the general U.S. adult population, Stanford-Binet IQ scores are approximately normally distributed with a mean of 100. Just 2.5% of U.S. adults score above 132 on this IQ test. What is the standard deviation of the IQ scores? A) 1 B) 2. C) 16 D) 32 E) 116
Brand Purchased Reebok Nike Other Type of Purchase
Cash 5% 10% 5% Credit Card 40% 15% 25%
y^
x
- The graph at the right shows a normal curve with mean 10 and standard deviation 1. What is the value of the shaded area? A) 0. B) 0. C) 0. D) 0. E) 0.
- The 381 students in Quant II took a 35 question exam. The average score was 28.4 and the standard deviation was 2.6. Class policy is that you must get 88% or more correct to get an A. Here that means you must get 31 questions or more correct. The distribution of scores is approximately a normal curve. About how many students got A’s on this test? A) 20 B) 29 C) 37 D) 48 E) 61
- A balanced coin is flipped once. Let y be the number of tails obtained. What is the variance of y? A) 1/ B) 1/ C) 1/ D) 1 E) None of the above.
- A manufacturer produces bags of candy with a printed label weight of 20 ounces. The actual weights vary according to a normal distribution with mean 20.49 ounces and standard deviation 0.21 ounces. What percentage of the bags weigh less than the label weight? A) 0% B) 1% C) 2.5% D) 5% E) 16%
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D) The least-squares regression line is found by minimizing the sum of squared residuals. E) After fitting a linear regression model, we can see how the predictor variable causes the response variable to change, i.e. there is a cause-and-effect relationship between the predictor and the response.
- The graph at the right shows the movements of a certain stock price over 48 days. Which of the following gives the value of the lag one autocorrelation coefficient? A) −0. B) −0. C) +0. D) +0. E) +1.000 (^10203040)
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Time
Stock Price
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