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Final Exam, May 12, 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 (Optional codes under LMN) on the answer sheet.
- A universe consists of 8 elements. How many samples of size 3 are possible?
A) 8 B) 24 C) 6720 D) 40, E) None of the above.
- A statistic is a numerical characteristic of a population.
A) True B) False
- 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 80.0 and standard deviation 7.8, what exam score corresponds to the highest F grade? A) 50 B) 55 C) 60 D) 65 E) 70
- Longitudinal data were collected on a continuous variable from a stable process. Unfortunately, they were given to us only in numerical order from smallest value to largest value rather than in time order. Which of the following could we reasonably produce from the data as given? I. the one-sample t -statistic for testing H 0 : μ = 55 II. the standard error of the mean III. the p -value for testing H 0 : μ = 100 A) I and II only B) II and III only C) I and III only D) I, II, and III E) None of the above.
Q
II
- 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.
- The model GP100M = −1.3 + 0.0025Weight + 0.7Trans is obtained from fitting Gallons per 100 miles to Weight and Transmission type for a number of cars. Here Weight is in pounds and Transmission type is an indicator variable with Trans = 1 for automatic transmissions and = 0 for manuals. A new car, the Ford Contour, comes on the market. It weighs 2910 pounds, has a 4 cylinder engine and a 4 speed automatic transmission. What does the regression model predict for the Ford Contour in gallons per 100 miles? (Rounded to the nearest gallon.) A) 6 B) 7 C) 15 D) 16 E) 17
80 90 100 110
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Fitted
Residual
M M M (^) M M M MM F M M^ F F F F^ F F (^) F (^) F F
- 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.
- The use of the finite population correction factor ( fpc ), decreases the standard error of the mean to account for the effects of sampling without replacement. A) True B) False
- 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
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Time
Series Value
- Consider a Binomial distribution with n = 3 and π = 0.3. What is the chance of at most one success? A) 0. B) 0. C) 0. D) 0. E) None of the above.
- The normal probability plot for the percentage changes of the daily Chrysler stock price data is shown below:
This plot shows that: A) normality of the percentage changes is strongly supported. B) normality of the percentage changes is not supported since the curvature in the plot indicates that the distribution is strongly skewed towards the high values. C) normality of the percentage changes is not supported since the curvature in the plot indicates that the distribution is strongly skewed towards the low values. D) normal scores plots cannot be used with percentage change data. E) normal scores should have been calculated for the original stock prices.
- The Central Limit Effect applied to a Binomial variable y^ from n^ trials of a Bernoulli process says that for large n the distribution of y is approximately normal with mean π and standard deviation.
A) True B) False
-5 0 5
3 2 1 0
NScores
π ( 1 – π) -------------------- n
- 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
- A survey is to be carried out using a simple random sample. Assume that the universe is very large. We need to be 95% confident that our estimate of a certain proportion has a margin of error of ±0.02 (that is, ±2 percentage points). How large a sample do we need? A) 50 B) 95 C) 836 D) 1190 E) 2501
- We have observed 9 values of a stable process and obtained a sample mean of 100.5 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)
- A result is said to be statistically significant when the observed value of a test statistic is close to the value specified by the null hypothesis. A) True B) False
- We need to find the critical value, t 1 −α/2, for a t -test with 11 degrees of freedom. The alternative is two-sided. What is the value of t 1 −α/2 if the significance level is 5%? A) −1. Β) −2. C) 1. D) 2. E) None of these
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 a simple random sample, increasing the sample size will decrease the margin of sampling error (other things being equal). A) True B) False
- Type I error is failing to reject a false null hypothesis.
A) True B) False
- Suppose that we have two independent estimates, y 1 and y 2 , of μ 1 and μ 2. Both means are based on 10 observations. The standard error of y 1 is 2.4 and of y 2 is 2.1. What is the standard error of y 1 − y 2? A) 0. B) 1. C) 1. D) 3. E) 10.
- A simple random sample of size 100 from a large universe yielded a sample proportion of 0.40. Find the upper endpoint of the 99.7% confidence interval for the population proportion π. A) 0. B) 0. C) 0. D) 0. E) 0.
- A new marketing strategy is tested against the one in present use. The results reported that the p -value was 0.02. Which one of the following statements is correct? (Here the null hypothesis is that the two strategies are no different.) A) H 0 should be rejected at the 1% significance level. B) H 0 should be rejected at both the 1% and 5% significance levels. C) H 0 should not be rejected at the 5% significance level. D) H 0 should not be rejected at the 10% significance level. E) H 0 should not be rejected at any significance level less than 2%.
- The frame is the list of elements from which a sample is drawn.
A) True B) False
- In an experiment a class of students were asked to guess the age of their professor. 190 of them were given no additional information but 189 were told the ages of the professor’s three children. 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) 5. C) 12. D) 302 E) Cannot be determined from the information given.
- Referring to the previous problem: What is the critical t value 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.
- Which one of the following displays the cross-sectional characteristics of a process?
A) Deming’s PDCA wheel B) standard deviation chart C) flow diagram D) cause-and-effect diagram E) density histogram
- In a probability survey, increasing the sample size will decrease nonsampling errors.
A) True B) False
Group n
Mean Guess of Age (years)
Standard Deviation SE Mean
No information 190 48.14 5.557 0. Given Ages of Kids 189 53.97 3.201 0.
- Which of the following tools would be useful for a longitudinal analysis of a process?
I. Control charts for means II. p -charts III. Sequence plots A) I only B) II only C) III only D) I, II, and III E) None of the above.
- A sequence plot of 5 years of monthly data is shown below. Which of the following best describes the plot?
- Five percent of the products produced by a stable process are defective. If a sample of 4 items is taken, what is the probability that the sample contains at least one defective? (to the nearest hundredth) A) 0. B) 0. C) 0. D) 0. E) 0.
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Month
L JK
I EFGH D C AB L
K
IJ H FG DE C LAB JK
I H
G
F E D C B LA K
IJ H EFG D C AB L JK
HI
FG E D C AB
A=Jan, B=Feb, C=Mar, D=Apr,... I=Sep, J=Oct, K=Nov, L=Dec
A) random B) meandering C) seasonal D) straight-line trend E) straight-line trend plus seasonal
