Download Final Exam Dec. 11, 1995: Quant II Form AB and more Exams Business Statistics in PDF only on Docsity!
Final Exam Dec. 11, 1995, Quant II Form AB
The 40 exam questions and answer sheet are both to be turned in at the end of the exam. Code your name, ID number, and Test Form on the answer sheet. Code your Section number under OPTIONAL CODES in positions L M N.
- Incomes were reported in whole thousands of dollars. The histogram of the incomes is shown below. Based on the histogram, how many incomes are below 18 thousand dollars? Histogram of Income N = 10
Midpoint Count 10.00 1 * 15.00 5 ***** 20.00 3 *** 25.00 1 * A) 1 B) 3 C) 5 D) 6 E) Cannot be answered with the information given.
- A survey is to be carried out using a simple random sample from a very large universe. We need to be 99.7% confident that our estimate of a certain proportion has a margin of sampling error of ±0.02 (that is, ±2 percentage points). How large a sample do we need? A) 95 B) 836 C) 1190 D) 2501 E) 5626
- The regression model where x and z are both continuous variables is best described as A) one straight line B) two parallel lines C) two non-parallel lines D) a quadratic curve E) a regression plane
- A Type I erro r is rejecting a true null hypothesis.
A) True B) False
y ˆ^ = b 0 + b 1 x + b 2 z
Q
II
- The use of the finite population correction factor ( fpc ), increases the standard error of the mean to account for the effects of sampling without replacement. A) True B) False
- Consider the special “quadratic” model. Let r^ be the correlation coefficient
between x^ and y^ and let r * be the correlation coefficient between x^2 and y. Let be the standard deviation for the x^2 variable, that is, first the x ’s are squared and then the standard deviation is found for the squares. If we use least squares to fit the special “quadratic” model shown above, which of the following gives the correct value for b 1? A) r B) r *
C)
D)
E)
- We have observed 9 values of a stable normal process and obtained a sample mean of 100. and sample standard deviation of 0.23. We need to estimate the mean of the process. What is the value of the upper endpoint of a 95% confidence interval for the process mean? A) B) C) D) E)
- Multiple call-backs to nonrespondents are not possible in
A) a probability survey B) a nonprobability survey C) a telephone survey D) a confidential mail survey E) an anonymous mail survey
y ˆ^ = b 0 + b 1 x^2 s (^) x 2
r s (^) y (^) s^ --- (^) x -
r *
s (^) y (^) s^ --- (^) x -
r *
s (^) y s -----^ x -^2
100.5 +2.306 ×( 0.23)
100.5 +1.860 ×( 0.23)
100.5 +1.860 ×( 0.23 ⁄( 9 ))
100.5 + 2 ×( 0.23 ⁄( 8 ))
100.5 +2.306 ×( 0.23 ⁄( 9 ))
- In an experiment a class of students were asked to guess the age of their professor. 172 of them were given no additional information but 152 were told the year of the professor’s graduation for his BA and Ph.D degrees. Here are the results:
What is the value of the t -statistic for testing the null hypothesis of no difference between the two group means? Here H 0 : μinfo − μnoinfo = 0. A) 0. B) 6. C) 9. D) 13. E) 313
- Refering to the previous problem: What is the critical t value, t 1 −α , for testing against a one-sided alternative (that the group with more information would have a higher mean, H 1 : μinfo−μnoinfo >0) at the 5% significance level? (We would reject the null hypothesis if our observed two-sample t -statistic is greater than this value.) A) 1. B) 1. C) 1. D) 2. E) 2.
- The frame is the list of elements from which the sample is drawn.
A) True B) False
- The standard deviation of the distribution of a sample proportion p from n trials of a Bernoulli process is largest when π = 0.5. A) True B) False
- Nonsampling error is the difference between the value of a sample estimate and a corre- sponding equal complete coverage value that is due to some cause other than the sampling process. A) True B) False
Group n
Mean Age Guess (years)
Standard Deviation
No information given 174 47.3 6. Given BA & Ph.D Years 152 54.2 6.
- A universe consists of 350 elements. How many different samples of size 349 are possible?
A) 1 B) 349 C) 350 D) 349! E) 350!
- Suppose that 30 subgroups (samples) each of size 50 are selected from a Bernoulli process. If there are 150 defectives overall, what is the value of the upper control limit (UCL) for the p -chart for fraction defective? (Rounded to the nearest hundredth.) A) 0. B) 0. C) 0. D) 0. E) 0.
- The regression model where x and is a continuous variable, and z is a binary indicator variable is best described as A) one straight line B) two parallel lines C) two non-parallel lines D) a quadratic curve E) a regression plane
- The Central Limit Effect applied to a sample proportion p from n trials of a Bernoulli process says that for large n the distribution of p is approximately normal with mean n π and standard deviation. A) True B) False
- The equal complete coverage is the set of measurements that would be obtained if the survey procedures were used on every element in the universe. A) True B) False
- Deming’s Red Bead Game demonstrated that variation can be reduced in any process.
A) True B) False
- A parameter is a numerical characteristic of a population.
A) True B) False
y ˆ^ = b 0 + b 1 x + b 2 z
n π ( 1 – π)
- 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 smaller than 2.98 inches? A) 0. B) 0. C) 0. D) 0. E) None of the above.
- The time it takes for an automatic car wash to wash a car varies according to a number of factors—is it a basic wash, a wash and wax, and so forth. Suppose that the distribution of individual wash times has a mean of 5 minutes and a standard deviation of 20 seconds. You are in line behind 9 cars waiting for a car wash. The first car begins its wash. What are the chances that you will have to wait more than 46 minutes before starting your car wash? A) 5% B) 16% C) 32% D) 95% E) 99.7%
- For the sequence 5, 4, 5, 7, 9, find the lag one autocorrelation. (Hint: The mean for the sequence is 6 and the standard deviation is 2.) A) 0. B) 0. C) 0. D) 0. E) 0.
- The graph below shows monthly salary versus years of experience for several employees. Salaries for males are plotted with plotting symbol M and females F. Let y be salary, x years of experience, and z an indicator variable for gender with z = 1 for Female and z = 0 for Male. Consider the regression model with equation = b 0 + b 1 x^ + b 2 z.^ Which one of the following statements is true? A) The coefficient b 0 represents the rate of increase of salary with years of experience. B) The coefficient b 2 represents the rate of increase of salary with years of experience. C) For employees with equal years of experience, b 0 is the difference between predicted sala- ries for females and for males. D) For employees with equal years of experience, b 1 is the difference between predicted sala- ries for females and for males. E) For employees with equal years of experience, b 2 is the difference between predicted sala- ries for females and for males.
- Refer to the previous problem. If numerical values for the regression coefficients are obtained by least squares, which one of the following statements is true? A) The quantity b 0 will be negative. B) The quantity b 1 will be negative. C) The quantity b 2 will be negative. D) The quantity b 0 + b 1 will be negative. E) The quantity b 0 + b 2 will be negative.
y ˆ
0 5 10
Years Experience
Monthly Salary
M
F F
M
F
M
F
M
M
F F
M
