STAT303: Secs 508-510Fall 2004Exam #2Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. Be sure to write your instructor’s name in the space provided on the scantron and your name beneath.3. 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.4. You will have 60 minutes to finish this exam.5. 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.6. This exam is worth 100 points, and will constitute 20 of your final grade.7. Good luck!1STAT303: 508-510 Exam #2, Form A Fall 20041. Which of the following is FALSE?A. A p-value is how often we would get dataas contradictory as we got even though H0is true.B. A p-value is a measure of the strength ofthe evidence against the null hypothesis.C. A p-value is the probability that the null hy-pothesis is rejected even though H0is true.D. A p-value can be used to perform a test ofhypotheses at any significance level.E. None of the above are false; all of the aboveare true.2. Let X ∼ N(4, 22). What is P (2 < X < 5)?A. 0.0228B. 0.5C. 0.5328D. 0.6915E. 0.85023. A 95% confidence intervalA. contains 95% of the sample meansB. contains all population means which wouldresult in the observed sample falling withinthe central 95% of the sampling distributionC. contains 95% of the population meansD. contains 95% of the populationE. none of the above4. Using α = 0.05 means thatA. we will reject H05% of the time.B. we will commit a Type I error 5% of thetime.C. we will be wrong (i.e.,make the wrong de-cision) 5% of the time.D. All of the above are true.E. Exactly two of the above are true (exclud-ing D).5. Supposed we tested H0: µ = 10 vs. HA: µ > 10and got a p-value = 0.003. Which of the follow-ing would be the best conclusion?A. Reject H0at the 0.3% level and concludethat the true mean is not 10.B. Reject H0at the 0.3% level and concludethat the true mean is greater than 10.C. Reject H0at the 5% level and conclude thatthe true mean is not 10.D. Reject H0at the 5% level and conclude thatthe true mean is greater than 10.E. Reject H0at the 5% level and conclude thatthe true mean is greater than 0.3%.6. Which of the following are true?A. Random chance will cause a statistic to varyfrom sample to sample.B. All parameters have sampling distributions.C. A parameter is a function of sample out-comes.D. All of the above are true.E. None of the above are true.7. Suppose we have a binomial population with thefixed number of trials n = 25 and the true prob-ability of a success π = 0.30. What is the sam-pling distribution of the sample proportion (orprobability), p?A. N(µp= 0.30, σ2p=p0.30(1 − 0.30)/252)B. N(µp= 0.30, σ2p= (0.30/√25)2)C. µp= 0 .30, σp=p0.30(1 − 0.30)/25, butwe can’t say the shape is approximatelynormal since the sample size (number of tri-als) is less than 30.D. µp= 0 .30, σp=p0.30(1 − 0.30)/25, butwe can’t say the shape is approximatelynormal since nπ < 10.E. N(µp= 0.30, σ2p= (0.30/25)2)90% CI: (4.01057, 7.58943)95% CI: (3.61245, 7.98754)99% CI: (2.73322, 8.86678)8. What is the correct range of the p − value fortesting H0: µ = 4 vs. HA: µ 6= 4 given thethree confidence intervals for µ above?A. p-value> 0.10B. 0.10 > p-value> 0.05C. 0.05 > p-value> 0.01D. p-value< 0.01E. You need a test statistic value to determinethe p − value2STAT303: 508-510 Exam #2, Form A Fall 20049. What is P (X = 2) + P (X = 4) + P (X = 6) ifX ∼ N (4, 22)?A. approximately 68%B. approximately 95%C. at least 75%D. at least 89%E. 0--------------------------------X | -2 | 0 | 2 | 3--------------------------------p(X) | 0.4 | 0.3 | 0.2 | 0.1--------------------------------10. What are the mean, µX, and median,˜X, for thedistribution above?A. µX= −0.1,˜X = 0B. µX= 1.5,˜X = 1.5C. µX= −0.1,˜X = −0.1D. µX= 0,˜X = 0E. µX= 1.5,˜X = 011. What is the probability of getting two indepen-dent observations less than 0 in the distributionabove?A. 0.4B. 0.14C. 0.21D. 0.16E. 0.812. What are the ±zα/2’s for a 78% confidence in-terval, i.e., P (−z∗< Z < z∗) = 0.78 whereZ ∼ N (0, 12)?A. ±0.11B. ±0.5438C. ±0.77D. ±0.8133E. ±1.2313. If H0: µ = µ0vs. HA: µ 6= µ0is rejected at the5% level, thenA. it would also be rejected at the 1% level.B. we can’t say if it would be rejected at the10% level.C. µ0would not be in a 95% confidence inter-val for µ.D. All of the above would be true.E. None of the above would be true.14. Let p30∼ N (0.8, 0.0732). What is the P (p30<0.6)? (Note: n = 30.)A. 0.0031B. -2.74C. 0.7402D. 0.9969E. Since we don’t know π, we don’t know nπand n(1 −π) are greater than or equal to 5,so we can’t normalize p30.15. Which of the following best describes randomsampling?A. all of the observations from the populationare equally spread out in the sampleB. all possible samples of size n are equallylikelyC. all possible samples of size n are normallydistributedD. all of the observations from the populationare normally distributedE. all possible samples of size n are equallyspread out16. Why do we call the distribution of the samplemean, Xn, a sampling distribution?A. because it’s the distribution of the sampleof random observationsB. because we must take a sample just to getone random observationC. because we sample from the distribution tofind the sample meanD. because the distribution is only of a sample,not the whole populationE. because we can’t get the distribution of thewhole population of sample means, onlysamples17. Let X ∼ N(10, 32). What is P (X9> 13)?A. We can’t say since we don’t know if X9isnormal.B. 0.8413C. 0.1587D. 0.9987E. 0.00133STAT303: 508-510 Exam #2, Form A Fall 200418. Given that we’ve generated 20 80% confidenceintervals from the same distribution, as in thelast homework, which of the following is true?A. It’s impossible that all 20 will contain thetrue mean, µ, of the population since 80%is so far (different) from 100%.B. It’s possible that exactly 80% of these inter-vals contain the true mean, µ, of the popu-lation.C. If we looked at all 400 (20 intervals created20 times as in the homework), then exactly80% would contain the true mean, µ, of thepopulation since 400 is a much larger sam-ple than just 20.D. All of the above are true.E. None of the above are true.19. A 95% confidence interval for
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