STAT303 Secs 508–510Spring 2004Exam #2Form AInstructor: Julie Hagen Carroll1. Don’t EVEN open this until you are told to do so.2. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly on the scantron. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade ofzero on the exam. You must work alone.5. This exam is worth 100 points, and will constitute 20% of your final grade.6. Good luck!1STAT303 508–510 Exam #2, Form A Spring 20041. If you know that a hypothesis test is statisticallysignificant, you also knowA. the p-value is greater than α.B. the null hypothesis is rejected.C. the alternative hypothesis is proven true.D. All of the above are correct.E. Only two of A, B and C are correct.2. In which of the following is the sample pro-portion, p, NOT approximately normally dis-tributed?A. n = 30, π = 0.75B. n = 50, π = 0.80C. n = 25, π = 0.50D. n = 30, π = 0.40E. p would be approximately normally in all ofthe situations above.3. Why do we need the distribution of our samplestatistic to be normally distributed?A. We don’t have to have them be normallydistributed. We just need to know whatthe distribution is.B. so we can find probabilities and percentilesC. so we can create confidence intervalsD. All of the aboveE. Only two of the above.4. What are the correct z-scores (critical values) touse for a 48% confidence interval for the truepopulation proportion, π?A. 0.48 and 0.52B. ±0.48C. ±0.6844D. ±0.05E. ±0.645. Which of the following is the best interpretationof the p-value for H0: µ = 50 vs. HA: µ < 50with ¯x = 48 and the p-value = 0.001.A. 0.1% of the time we will reject the the nullhypothesis.B. 0.1% of the time we will get a sample mean,¯x = 48 or more, when the true mean, µ =50.C. 0.1% of the time we will get a sample mean,¯x = 50 or more, when the true mean, µ =48.D. 0.1% of the time we will get a sample mean,¯x = 48 or less, when the true mean, µ = 50.E. 0.1% of the time we will get a sample mean,¯x = 50 or less, when the true mean, µ = 48.6. Suppose the sample size in the previous problemwas 30 (p-value = 0.001). If the sample size hadbeen 50 instead (and the sample mean and stan-dard deviation stayed the same), which of thefollowing would be true?A. The sample would be more normal.B. The p-value would be more normal.C. The p-value would be larger.D. Two of the above are true.E. None of the above would be true.7. Suppose you’re testing H0: µ = 5 vs. HA:µ > 5, you get a sample mean, ¯x = 4, from asample of size 25 and you know the populationis normal with a standard deviation is 2. Whatis the correct p-value for this test?A. You can’t determine it without a computerprogram (output).B. 0.9938C. 0.0062D. between 0.01 and 0.005 since it’s a t-testE. 0.69158. Let X ∼ N (18, 72) and X4is the sample meanfrom a sample of size 4. Which of the followingis true?A. P (X > 18) > P (X4> 18)B. P (X > 20) > P (X4> 20)C. P (X < 20) > P (X4< 20)D. P (X < 11) = 2 ∗ P (X4< 11)E. None of the above are true statements.2STAT303 508–510 Exam #2, Form A Spring 20049. What is the purpose of confidence intervals?A. They give us a range of plausible values forour sample statistic.B. They give us an idea of the size of the effect(e.g., difference between µ0and ¯x).C. They help us determine whether a statis-tically significant result has any practicalsignificance.D. All of the above are true.E. Only two of the above are true.10. When is 30 not a large enough sample for thesample statistic to be approximatley normallydistributed?A. when the sample has at least one large out-lierB. when the population sampled is highlyskewedC. when the population proportion is 70% ormoreD. All of the above are correct answers to thequestion.E. Only 2 of the first 3 are correct answers tothe question.11. If I know that the p-value = 0.043 for the testH0: µ = 10 vs. HA: µ 6= 10, thenA. I can conclude that the true mean is not 10at the 5 and 10% significance levels.B. I can say the results are statistically signif-icant for any significance level.C. I know that 10 would fall in the 90 and 95%confidence intervals created from the samedata.D. All of the above are true.E. Only two of A, B and C are true.12. Which of the following would give us the MOSTpower in a hypothesis test?A. α = 0.01 and n = 100B. α = 0.05 and n = 100C. α = 0.01 and n = 50D. α = 0.10 and n = 50E. α = 0.10 and n = 10013. What is the 70thpercentile of the distribution ofsample proporitons, p ∼ N (0.8, 0.042)?A. 0.56, 70% of 0.8B. 0.828, 0.8 + 0.70 ∗ 0.04C. 0.821, 0.8 + 0.525 ∗ 0.04D. 0.830, 0.8 + 0.758 ∗ 0.04E. 0.028, 0.70 ∗ 0.0414. A fast food franchiser is considering building arestaurant in a certain location. Based on fi-nancial anyalyses, a site is acceptable only if thenumber of pedestrians passing the location av-erages more than 100 per hour. The numberof pedestrians observed for each of forty hourswas recorded and had a standard deviation of12. Which type of statistical test should we em-ploy to decide if the site is acceptable?A. Case 10 since this test reduces the variabil-ity.B. Case 3 since the sample size is large (> 30)and we are testing one mean.C. Case 8 since we can assume that the vari-ances are both 122.D. Case 9 since we are not told that the vari-ances are equal.E. Case 1 since the population standard devia-tion is known and we are testing one mean.90% (162.47, 208.13)95% (158.10, 212.50)99% (149.55, 221.05)15. Suppose these three confidence intervals for thepopulation mean, µ, are the only informationyou have for testing H0: µ = 220 vs. HA:µ 6= 220. What is the range of the p-value forthis test?A. p-value> 0.10B. 0.10 > p-value> 0.05C. 0.05 > p-value> 0.01D. p-value< 0.01E. It’s impossible to tell without the test.16. The 95% confidence interval for µ in the previousproblem is (158.1, 212.5). Which of the followingis the best interpretation of this interval?A. 95% of the time an interval like this (us-ing the same calculations, sampling methodand population) will contain 220.B. 95% of the time an interval like this (us-ing the same calculations, sampling methodand population) will contain µ, the truepopulation mean.C. The probability of this interval containingthe true mean, µ, is 95%.D. 95% of the time an interval like this (us-ing the same calculations,
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