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STAT303 Secs 508–
Fall 2001
Exam
Form A
Instructor: Julie Hagen Carroll
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- There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your answers clearly on the exam. Multiple marks will be counted wrong.
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- Which of the following is an example of a matched pairs design?
A. A teacher compares the pre-test and post- test scores of students. B. A teacher compares the scores of students using a computer-based method of instruc- tion with the scores of other students using a traditional method. C. A teacher compares the scores of students in her class on a standardized test with the national average score. D. A teacher compares her class’ average score on a standardized test with the national av- erage score. E. A teacher calculates the average of scores of students on a pair of tests and compares the two averages.
- The sample size affects many things. Which of the following does it NOT affect?
A. the width of all of the confidence intervals covered in class B. the chance of making a Type II error C. the α-level D. the p-value E. All of the above are affected.
- Which would be a Type II error in the test: H 0 : μ 1 = μ 2 vs. HA : μ 1 > μ 2?
A. claiming that μ 1 < μ 2 B. failing to prove μ 1 > μ 2 when it’s really true C. claiming that μ 1 < μ 2 when it’s really greater D. claiming that μ 1 > μ 2 when it’s not true E. failing to prove μ 1 < μ 2 when it’s really true
- A Simple Random Sample of 25 male faculty members at a large university found that 10 felt that the university was supportive of female and minority faculty. An independent SRS of 20 female facutly found that only 5 felt that the university was supportive of female and minor- ity faculty. A 95% confidence interval for the difference in the true proportions of male, πM , and female, πF , faculty at the university who felt that the university was supportive of female and minority faculty at the time of the survey is:
- 15 ± 0 .270. If we want to test H 0 : πM = πF vs. HA : πM 6 = πF , what conclusion should we make at the 5% significance level?
A. We cannot decide without running a test of hypotheses. B. Since both sample proportions (0.4 for males and 0.25 for females) are not less than 0.05, we fail to reject H 0 and conclude we could not prove that the true proportions are different. C. Since the sample proportions (0.4 for males and 0.25 for females) are not equal, we re- ject H 0 and conclude that the true propor- tions are not equal. D. Since the confidence includes 0, we fail to reject H 0 and conclude that we could not prove the true proportions are different. E. Since the confidence does not include 0, we reject H 0 and conclude that the true pro- portions are different.
- Which of the following is/are necessary assump- tions for the data and test procedure above?
A. We must have at least 30 in each sample. B. Since the sample sizes are less than 30, the data must be normal. C. The standard deviations (variances) must be equal. D. All of the above are necessary. E. None of the above are necessary.
- The US Golf Association regularly tests golf equipment to ensure that it conforms to USGA standards. Suppose it wishes to compare the mean distance traveled by four different brands of golf balls when struck by a driver. How should they gather their data?
A. get the data from the 4 different companies and run an ANOVA test to compare the means B. poll golfers at a randomly selected golf course and record their brand and average drive (distance the ball is driven) C. take a random sample of each brand and have a golfer hit all of them, in random or- der D. take a random sample of gold course and record which brands are used E. take a random sample of each brand and have four golfers hit all of them, in random order
- A sportswriter wished to see if a football filled with helium travels farther, on average, than a football filled with air. He used 18 adult males, randomly divided into 2 groups: one kicked the helium filled footballs, the other kicked air filled footballs. What are the correct hypotheses to test?
A. H 0 : μ = X vs. HA : μ 6 = X, where X is the true average distance an air filled football travels when kicked B. H 0 : μair = μhelium vs. HA : μair > μhelium C. H 0 : μair = μhelium vs. HA : μair 6 = μhelium D. H 0 : μair = μhelium vs. HA : μair < μhelium E. H 0 : πair = πhelium vs. HA : πair > πhelium, where π is the proportion of field goals kicked
- If we can assume that the two groups are inde- pendent and the data is approximately normal, what else would help us determine if helium filled footballs travel farther?
A. if the kickers don’t know which type of foot- ball they kicked, air or helium B. if the kickers don’t know who the sportswriter is (or what paper he’s with) C. if the kickers don’t know where the uprights (goal) are D. if the kickers don’t know how far others kick E. if the kickers don’t know if they made the team or not
- Suppose we have two SRS’s from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For the purposes of comparing the two means we can use the pooled t-test procedure if
A. the means for the two populations are ac- tually equal. B. the standard deviations for the two popula- tions are actually equal. C. the sample means for the two populations are equal. D. the sample sizes are the same. E. Two of the above are correct.
- A researcher is studying treatments for agoro- phobia with panic disorder. The treatments are to be the drug Imipramine at doses of 1.5mg per kg of body weight and 2.5mg per kg of body weight. There will also be a control group given a placebo. Thirty patients were randomly di- vided into 3 groups of 10 each. After 24 weeks of treatment, each of the subject’s symptoms were evaluated through a series of tests, where a high score indicates a lessening of symptoms. Assume the data for the 3 groups are independent and approximately normal.
Group Mean Test Score Std Dev. control 75.7 12. 1.5mg 84.1 18. 2.5mg 102.4 20.
The p-value for this test is 0.007. Which of the following is correct?
A. The standard deviation for the 2.5mg dose is not equal to the other two. B. The true variances for the three groups are not all equal. C. The true means for the three groups are not all equal. D. The 2.5mg dose works the best since it has the largest mean test score. E. The 2.5mg dose works 7% better than the other two.
- The experiment above used a control group. Why is that a good idea?
A. We need a control to determine the size of the effect. B. Having a control enables us to control the effect of confounding variables. C. Having a control makes the differences more statistically significant. D. Having a control makes the assumption of independence and normality more reliable. E. Having a control enables us to control the effect of the drug.
- A political analyst was curious if younger adults were becoming more conservative. He decided to see if the mean age of registered Republicans was lower than that of registered Democrats. He selected a SRS of 128 Republicans from a list of those registered and got a mean xR = 39 years with a sd sR = 8. He also took a SRS of 200 registered Democrats and found the mean to be xD = 40 years with a sd sD = 10. The result- ing p-value for testing whether the average age of Republicans is less than that of Democrats is 0.171. Which of the following is the best inter- pretation of this p-value?
A. 17.1% of the time we would see a sample mean age of Republicans at least this much smaller than that of Democrats even though the true mean ages are the same. B. 17.1% of the Republicans are younger than the average Democrat. C. 17.1% of the time we would see a sample mean age of Republicans at least this dif- ferent from that of Democrats even though the true mean ages are the same. D. The Republicans are 17.1% younger than the Democrats. E. 17.1% of the time we would find Republi- cans younger than Democrats even though they’re the same age on average.
- If the sample mean age of Republicans was 36 instead of 39, which of the following would be true (given everything else stayed the same)?
A. More than 17.1% of the Republicans would be younger than the average Democrat. B. The test would no longer be valid since the sample means are so different. C. The p-value would be smaller. D. The results would be more significant. E. Two of the above are correct.
- Twelve runners are asked to run a 10 kilometer race on each of two consecutive weeks. In one of the races, picked at random, the runners wear one brand of shoe and another brand in the sec- ond race. The runners are asked to run their best in both races and their times are recorded. Which method should we use to test whether the brand of shoe has an effect run time?
A. ANOVA F -test, assuming the data is nor- mal. B. Case 2: the 1-sample test of the mean, as- suming that the data is normal. C. Case 10: the paired test, pairing the brands by runner. D. Non-parametric case for paired data since we don’t know if the data is normal. E. Case 9: the 2-sample test, assuming that the data is normal.
- The pooled t-test and the 2-sample test for pro- portions pool some of the information. Why do we ‘pool’?
A. We don’t know the true value, so we have to guess. B. We can’t assume that they’re equal (either the sd’s or the p’s), so we need a better estimate. C. We get better estimates. D. It makes the data more random (it comes from a ‘pool’ of choices). E. None of the above are correct.
- A SRS of size 100 is taken from a population hav- ing proportion 0.8 of successes. An independent SRS of size 400 is taken from a population hav- ing proportion 0.5 of successes. The sampling distribution for the difference in the sample pro- portions, p 1 − p 2 , has mean
A. 0. B. 0. C. 0. D. 0. E. 0.
1A,2C,3B,4D,5E,6C,7E,8B,9C,10D,11D 12A,13B,14C,15B,16A,17E,18D,19C,20A
