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STAT303 Sec 508-
Spring 2007
Exam
Form A
Instructor: Julie Hagen Carroll
October 10, 2007
- Don’t even open this until you are told to do so.
- Please PRINT your name in the blanks provided.
- There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your answers clearly. Multiple marks will be counted wrong.
- You will have 60 minutes to finish this exam.
- If you have questions, please write out what you are thinking on the back of the page so that we can discuss it after I return it to you.
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- This exam is worth the same as a regular exam (this may differ from section to section.
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- Suppose that it is commonly assumed that the mean flight from College Station to Houston is 25 minutes. However, you believe that the true average is greater than this. You randomly choose 30 flights to take and record their times. The mean of your sample is 27. What would be a Type I error?
A. Concluding that the mean is greater than 25 when it really is 25 minutes B. Concluding that the mean is not greater than 25 when the true mean is 24 C. Concluding that the mean is not greater than 25 when the true mean is 26 D. Concluding that the true mean is 24 when the true mean is 25 E. Two of the above are true.
- The following are confidence intervals for 1 - 2 com- puted from the same data:
90% CI = (0.02, 0.09) 95% CI = (0.01, 0.12) 99% CI = (-0.03, 0.14)
Based on the intervals above, if we were to test H 0 : π 1 = π 2 vs. HA : π 1 6 = π 2 , what would be the corre- sponding p-value?
A. p-value > 0. 10 B. 0. 10 > p-value > 0. 05 C. 0. 05 > p-value> 0. 01 D. p-value < 0. 01 E. You need a test statistic value to determine the p-value.
- An insurance company is conducting a study compar- ing the average number of accidents for females and males. The company wants to show on average females have less accidents than males to justify lower rates for females. What is the appropriate hypothesis?
A. H 0 : μf emale = μmale vs. HA : μf emale 6 = μmale B. H 0 : πf emale = πmale vs. HA : πf emale 6 = πmale C. H 0 : μf emale = μmale vs. HA : μf emale > μmale D. H 0 : μf emale = μmale vs. HA : μf emale < μmale E. H 0 : πf emale = πmale vs. HA : πf emale < πmale
- A bank wonders whether omitting the annual credit card fee for customers who charge at least $5000 in a year would increase the amount charged on its credit card. The bank makes this offer to a simple random sample of 500 existing credit card customers. The bank then compares the amount charged this year with the amount charged last year for each of these customers. What type of test should be used to analyze this study?
A. A two-sample test of proportions B. A one-sample t-test C. A two-sample t-test since the standard deviation is unknown D. A pooled t-test E. A paired t-test
- Suppose we want to test whether the proportion of pa- tients who come down with a cold during their hospi- tal stay is the same for patients taking Echinacea every day and patients on a placebo drug. One herb company wants to prove that it lowers the rate at which patients catch a cold, so we set up the hypotheses: H 0 : π 1 = π 2 and HA : π 1 > π 2 , where π 1 is the proportion of people taking the placebo who get a cold during their hospital stay and π 2 is the proportion of people taking Echi- nacea who get a cold. The resulting p-value is 0.2171. What does that mean in context of the problem?
A. The probability that Echinacea doesn’t keep you from catching a cold is 0.2171. B. The probability that we find a difference in propor- tions at least this small assuming that Echinacea doesn’t keep you from catching colds is 0.2171. C. Under repeated sampling, we would find that pa- tients taking Echinacea every day had the same rate of sickness as patients on a placebo 21.71% of the time, assuming Echinacea actually doesn’t keep you from catching a cold. D. Under repeated sampling, we would find that pa- tients taking Echinacea every day had at least this much lower rate of sickness about 21.71% of the time, assuming that Echinacea doesn’t keep you from catching a cold. E. Two of the above are true.
- Which of the following best describes the relationship between a (1 − α) ∗ 100% confidence interval for μ 1 − μ 2 and a 2-sided test of hypotheses for μ 1 = μ 2 some value?
A. There is no relationship between confidence inter- vals and hypothesis tests. B. If μ 1 or μ 2 fall within the confidence interval, we would reject the null. C. If μ 1 or μ 2 fall within the confidence interval, we would fail to reject the null. D. If the confidence interval contains 0, we would re- ject the null. E. If the confidence interval contains 0, we would fail to reject the null.
- The purpose of pairing in an experiment is to
A. make the samples independent. B. increase the degrees of freedom of the t-test so the test has more power. C. match the observations so that there is less chance of making an error. D. filter out the variability between the subjects. E. None of the above are correct.
- Suppose we suspect that strawberry ice cream has f ewer calories than chocolate. We then want to test H 0 : μc = μs vs. HA : μc > μs, where μc is the mean number of calories in different brands of chocolate ice cream and μs is the mean number of calories in different brands of strawberry ice cream. Suppose that we ran the test, we found an average difference in the number of calories of 9.42. What would be a good interpreta- tion of α in context of this problem?
A. α is the probability (over the long run) we con- clude that strawberry ice cream has fewer calories than chocolate ice cream when in fact it does. B. α is the probability (over the long run) we con- clude that strawberry ice cream and chocolate ice cream have the same number of calories when in fact they do. C. α is the probability (over the long run) we con- clude that the number of calories in chocolate ice cream is greater than the number of calories in strawberry ice cream when actually they have the same number of calories. D. α is the probability (over the long run) we con- clude that strawberry and chocolate ice cream have the same number of calories when in reality chocolate ice cream has more calories than straw- berry. E. α is the probability that over the long run, we find a difference in calories of 9.42 or more just by chance, assuming that chocolate and strawberry ice cream have the same number of calories.
- Suppose you wanted to find out whether there is a dif- ference between the proportion of people 55 and over who voted for an increase in Social Security taxes and the proportion of people under 55 who voted for it. What would your null and alternative hypotheses be?
A. H 0 : μ = 55 vs. HA : μ 6 = 55 B. H 0 : π = 55 vs. HA : π 6 = 55 C. H 0 : μ 1 = μ 2 vs. HA : μ 1 > μ 2 D. H 0 : μ 1 = μ 2 vs. HA : μ 1 6 = μ 2 E. H 0 : π 1 = π 2 vs. HA : π 1 6 = π 2
- The Computer-Assisted Hypnosis Scale (CAHS) is de- signed to measure a person’s susceptibility to hypno- sis. CAHS scores range from 0 (no susceptibility) to 12 (highest possible susceptibility). A study at the Univer- sity of Texas reported that their undergraduates had a mean CAHS score of μ = 11.2. Suppose that you want to verify that undergraduates at A&M are less suscep- tible to hypnosis than t-sips. Which of the following situations best describes a Type II error? (Hint: write- out the alternative hypothesis in words and then use the definition for Type II error).
A. Finding significant statistical evidence that the mean CAHS score for Aggies is less than 11.2 when the true mean is 11.5.
B. Finding significant statistical evidence that the mean CAHS score for Aggies is less than 11.2 when the true mean is 4.6. C. Not finding significant statistical evidence that the mean CAHS score for Aggies is less than 11.2 when the true mean is 11.5. D. Not finding significant statistical evidence that the mean CAHS score for Aggies is less than 11.2 when the true mean is 4.6. E. Two of the above are true.
- In which of the following situations can you NOT use the normal approximation to conduct the hypothesis test? A. n = 80, H 0 : π ≥ 0. 9 B. n = 20, H 0 : π ≥ 0. 5 C. n = 60, H 0 : π = 0. 8 D. Two of the above would be invalid for the normal approximation test. E. None of the above would be valid for the normal approximation test.
- Suppose you tested H 0 : μ 1 = μ 2 vs. Ha : μ 1 6 = μ 2. Your data consisted of two samples with ¯x 1 = 10 and x¯ 2 = 12 and the resulting p-value was 0.806. Which of the following is the best interpretation of the p-value for this test? A. There is an 80.6% chance that the two true means are equal. B. There is an 80.6% chance of seeing at least this big of a difference in sample means when the true means are equal. C. If we took many samples from these same popu- lations, 80.6% of the time we would fail to reject H 0. D. If we took many samples from these same popula- tions, 80.6% of the time we would see at least this big of a difference in true means when the sample means are equal. E. If we took many samples from these same popula- tions, 80.6% of the time we would see at least this big of a difference in sample means when the true means are equal.
- Why must we know the sampling distribution of our statistic of interest in order to test hypotheses? A. Because the sampling distribution must be finite in order to look up the values on the chart. B. Because we don’t know which chart/table to use until we know what the distribution of the test statistic is. C. Because we cannot create the test statistic in the first place unless we know what the mean and vari- ance of the statistic are. D. Because the mean of the statistic of interest is al- ways hypothesized to be 0. E. Two of the above are true. 1A,2C,3D,4E,5D,6E,7D,8D,9E,10E,11A, 12D,13B,14C,15E,16C,17E,18D,19A,20E,21B
