STAT303 Sec. 508-510Fall 2010Exam #2 Form AOctober 28, 20101. 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. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. If you have questions, please write out what you are thinking on the back of the page so that we can discussit after I return it to you.5. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zeroon the exam. You must work alone.6. When you are finished please make sure you have marked your CORRECT section (Tuesday 12:45 is 508,2:20 is 509, and 3:55 is 510) and FORM and 20 answers, then turn in JUST your scantron.7. Good luck!1STAT30X: 508-510 Exam #2 Form A Fall 20101. If we each generated 20 random samples from apopulation of N (4, 102). From these samples, wetested H0: µ = 4 vs. HA: µ 6= 4 at the 5% level.Which of the following would be true?A. There would be at least 1 rejection in the 20tests even though H0is true.B. There would be no rejections since the truemean is 4.C. The standard deviation is too large for thetest to have much power.D. Since we don’t know the sample size, we don’tknow what would happen.E. None of the above are true statements.2. An automatic grinding machine in an auto partsplant prepares axles with a target diameter µ =40.125 millimeters (mm). The machine has somevariability, so the standard deviation of the diame-ter is σ = 0.002 mm. What should we test to makesure the machine stays within specifications?A. H0: µ = 0.002 vs. HA: µ 6= 0.002.B. H0: µ = 40.125 vs. HA: µ 6= 40.125.C. H0: µ > 40.125 vs. HA: µ ≤ 40.125.D. H0: µ ≤ 40.125 vs. HA: µ > 40.125.E. H0: µ ≤ 40.125 vs. HA: µ ≥ 40.125.3. We test the null hypothesis H0: µ = 10 and thealternative HA: µ < 10, for a normal population.A random sample of 16 observations is drawn fromthe population, and we find the sample mean ofthese observations is ¯x = 12 with s = 4. Thep-value isA. 0.0228B. 0.9772C. 0.05 > p-value > 0.025D. 0.10 > p-value > 0.05E. 0.975 > p-value > 0.954. Which of the following is true?A. The range of the p-value is always (0, 1), zeroto one.B. We always assume the null hypothesis is true.C. The larger the sample size the more likely thealternative is true.D. All of the above are true statements.E. Only two of the above are true statements.5. The table below is a One-way ANOVA test to seeif region of the country has an effect on environ-mental voting outcome.| Senate environmental votes 1990Region| Mean Std. Dev. n------------+------------------------------------New Engl | 76.833333 17.104865 6Mtn West | 46.416667 32.120394 12other | 47.3125 23.569304 32------------+------------------------------------Total | 50.64 26.554342 50Analysis of VarianceSource SS df MS F Prob > F---------------------------------------------------Between 4684.895 A 2342.45 C 0.0326Within 29866.625 47 B---------------------------------------------------Total 34551.52 49 705.13Which of the following is the correct conclusionabout this test?A. The sample sizes are too different to assumethey are equal, so this is an invalid F -test.No conclusion can be made.B. The standard deviations are too different toassume they are equal, so this is an invalidF -test. No conclusion can be made.C. The New England area is more pro the envi-ronment than the other areas.D. At the 1% level, we can conclude that thereis no significant effect.E. None of the above.6. What are the missing values from the previousANOVA table?A. A = 3, B = 635.46, C = 3.69B. A = 2, B = 635.46, C = 3.69C. A = 2, B = 1637.32, C = 1.43D. A = 3, B = 1637.32, C = 1.43E. A = 2, B = 3047.58, C = 1.302STAT30X: 508-510 Exam #2 Form A Fall 20107. A small New England college has a total of 400students. The Math SAT scores are required foradmission and the mean score of all 400 students isµ = 620 with population standard deviation σ =60. A sample of students was taken and a 95%confidence interval yielded the interval 640 ± 5.88.We may concludeA. that the interval is incorrect. It is much toosmall.B. that if we repeated this procedure many,many times, only 5% of the 95% confidenceintervals would fail to include the Math SATscore of each of students at the college.C. that 95% of the time, the population meanwill be between 634.12 and 645.88.D. a biased sample was taken since it’s intervaldidn’t contain the population mean.E. none of the above.8. We suppose we test H0: µ1= µ2vs. HA: µ16= µ2and get a p-value = 0.086. Which of the followingstatements are correct?A. The true difference in the means would be ina 95% confidence interval but not in a 90%interval.B. At the 5% level we would conclude that themeans are the same.C. At the 10% level we would conclude that themeans are different.D. All of the above are correct.E. Only two of the above are correct.9. What is the range of the p-value for testing H0:µ1= µ2vs. HA: µ16= µ2if ¯x1= 12.2, s1= 9.3,n1= 15, ¯x2= 18.6, s2= 7.1, n1= 18 and the teststatistic is 2.241?A. 0.02 > p-value > 0.01B. 0.04 > p-value > 0.02C. 0.025 > p-value > 0.02D. 0.05 > p-value > 0.04E. p-value > 0.02510. Which of the following statements is correct?A. An extremely small p-value indicates that theactual data differs markedly (alot) from thatexpected if the null hypothesis were true.B. The p-value measures the probability that thenull hypothesis is true.C. The p-value measures the probability of mak-ing a Type II error.D. The larger the p-value, the stronger the evi-dence against the null hypothesis.E. More than one is true.11. Stress resistance, X (in lb/in2) for a certain typeof plastic sheet is normally distributed with mean,µX= 30 and standard deviation, σX= 2. Howlikely are we to get a sample of size n = 16 withmean, x = 28 or less, i.e., what is the p-value fortesting H0: µ ≥ 30 vs. HA: µ < 30.A. practically 0B. almost 1C. 0.1587D. 0.8413E. 0.022812. What does the p-value above tell us?A. how often we would get a mean of 30 whenthe true mean is 28B. how often we would get a mean of 30 or lesswhen the true mean is 28C. how often we would get a mean of 28 or lesswhen the true mean was at least 30D. how often we would get a mean of at least 28when the true mean was 30 or lessE. how often we would get a mean of at least 30when the true mean was 28 or less13. Which type of hypothesis test would we use to testthe
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