STAT303 Sec 508-510Fall 2007Exam #2Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. All graphs are on the last page which you may remove.3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark youranswers clearly. Multiple marks will be counted wrong.4. You will have 60 minutes to finish this exam.5. If you have questions, please write out what you are thinking on the back of the page so that we can discuss it afterI return it to you.6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on theexam. You must work alone.7. This exam is worth the 15% of your course grade.8. 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 to the correct pile for your section.9. Good luck!1STAT303 sec 508-510 Exam #2, Form A Fall 20071. What are the z critical values, the zα/2, for a 58% con-fidence interval?A. ±0.719B. ±0.58C. ±0.20D. ±0.61E. ±0.812. Which statement agrees with P (p40≥ 0.30) for p40∼N(0.25, 0.0682)? n = 40A. What sample proportion is the upper 30% of thispopulation with mean 0.25 and standard deviation0.068?B. How likely are you to get 30% or more if you sam-ple a population of 40?C. How likely are you to get a probability of 0.30if you sample a population with mean 0.25 andstandard deviation 0.068?D. How likely are you to get a sample proportion of30% or more if you take a sample of 40 from apopulation with mean 25% and standard deviation6.8%?E. Math doesn’t equate to words.3. A certain population follows a normal distribution withmean µ and standard deviation σ = 2.5. You collectdata and test the hypotheses:H0: µ = 1HA: µ 6= 1You obtain a p-value of 0.022. Which of the followingis true??A. A 95% CI for µ will include the value 1.B. A 95% CI for µ will include the value 0.C. A 99% CI for µ will include the value 1.D. A 99% CI for µ will include the value 0.E. We can’t determine since we can’t relate confi-dence intervals to tests of hypotheses.4. Let X ∼ N(1, 22). If the probability of getting oneX at least 2 units (not standard deviations) from itsmean (greater than 2 units above or below its mean) is0.3174, the probability of getting a sample mean of 4,X4, at least this far from its mean will beA. more, 0.9544.B. less, 0.0228.C. less, 0.0456.D. more, 0.6826.E. the same, 0.3174.90% (2.3265, 16.4735)95% (0.972, 17.828)99% (-1.694, 20.494)5. Using the information above, what is the correct rangeof the p-value if I wanted to test H0: µ = 0 vs. HA:µ 6= 0?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 determine thep-value6. What would be the range of the p-value if we were test-ing H0: µ = 17 vs. HA: µ 6= 17 instead, but still usedthe 3 confidence intervals 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 determine thep-value7. Let X ∼ N (7.2, 1.42). If we take a random sample ofsize 49 from this population, what is the distribution ofthe sample mean,X49?A. Since the sample size is large, > 30, we can say thedistribution will be approximately normal withthe same mean and standard deviation.B. Since the original data is normal, we can say thedistribution will be exactly normal with the samemean and standard deviation.C. Since the sample size is large, > 30, we cansay the distribution will be approximately normalwith the mean, µX= 7.2 and standard deviation,σX=1.4√49.D. Since the original data is normal, we can say thedistribution will be exactly normal with the mean,µX= 7.2 and standard deviation, σX=1.4√49.E.X ∼ N(7.2, 0.0292).8. What can we do to reduce the length of a 95% confi-dence interval for µ but leave the confidence level at95%?A. reduce the sample mean, ¯xB. reduce the sample size, nC. reduce the population standard deviation, σD. reduce the z critical value, zα/2E. Two of the above will reduce the length.2STAT303 sec 508-510 Exam #2, Form A Fall 20079. If we each generated 200 random samples from a pop-ulation of N(4, 102). From these samples, we created200 95% confidence intervals. Which of the followingis/are true?A. It is plausible that 14 of them didn’t contain 4.B. It is possible that all of them actually contained4.C. We would mostly likely have 10 intervals thatdidn’t contain 4.D. All of the above are true.E. Exactly two of the statements above are true.10. Which of the following statements is correct?A. An extremely small p-value indicates that the ac-tual data differs markedly from that expected ifthe null hypothesis were true.B. The p-value measures the probability that the nullhypothesis is true.C. The p-value measures the probability of making aType II error.D. The larger the p-value, the stronger the evidenceagainst the null hypothesis.E. None of the above statements are true.11. It’s almost Halloween and pirates abound. The follow-ing table gives the type, value and probability (basedon the count) of a particular treasure chest. What arethe mean and median value of the jewels?type | Emerald | Ruby | Diamond | Other |---------------------------------------------value | $450 | $500 | $1000 | $300 |---------------------------------------------prob | 0.4 | 0.2 | 0.3 | 0.1 |A. µ = $1237.50 and˜X = $500B. µ = $610 and˜X = $500C. µ = $6100 and˜X = $500D. µ = $610 and˜X = $475E. µ = $750 and˜X = $75012. Assuming each grab is independent, how likely is a pi-rate to reach in a get exactly one emerald, one rubyand one diamond? It doesn’t matter if he reaches in 3times for one stone each or gets 3 stone with one grab.A. 0.9B. $1950C. 0.024D. 0.24E. 0.25313. Which of the following best describes the relationshipbetween a (1 − α)100% confidence interval for µ and a2-sided test of hypotheses for µ = some value, µ0?A. There is no relationship between confidence inter-vals and hypothesis tests.B. If the hypothesized value, µ0, falls within the con-fidence interval, we would reject the null.C. If the hypothesized value, µ0, falls within the con-fidence interval, we would fail to reject the null.D. If the confidence inteval contains 0, we would re-ject the null.E. If the confidence interval contains 0, we would failto reject the null.14. Let X be the distribution of
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