Intro to Statistics Final Exam: Questions with Answers | STAT 1222, Exams of Statistics

Download Intro to Statistics Final Exam: Questions with Answers | STAT 1222 and more Exams Statistics in PDF only on Docsity! STAT1222 Final Exam May 3, 2007 The following is used for questions 1, 2 and 3. Given below are the ages of motorcyclists at the time they were fatally injured in traffic accidents. 17 38 27 14 18 16 21 1 Find the mean of the data. Ks (a) 18.20 (b) 20.58 cey) 21.57 (d) 25.65 (e) 29.32 . 2 Find the standard deviation of the sample data. (a) 1.25 (b) 335 f (c) 678“ 6 10.25 a I 3 Find the median of the data. -<. @ STAT1222 page 2 of 13 May 3, 2007 Use the following to answer questions 4, 5 and 6. The IQ scores have a mean of 100 and a standard deviation of 15. 4 According to Chebycheb’s Theorem, what percentage of people will have IQ scores between 70 and 130? ¥ é rf” (a)? At least 75% ‘~¢b) At most 60% (c) At least 50% {d) At most 40% {e) At most 20% 5 If the distribution of the IQ scores can be approximated by normal distribution, then approximately what percentage of people will have 1Q scores greater than 115? .. 6.5% 16% 25% 54% 90% then - 6 The zscore of a person with TQ score of 140 is. (a) 2=0.00 (b) 2= 1.25 (ce), 2 = 2.00 (dy 2 = 267 Ye) 253.15 STAT1222 page 5 of 13 May 3, 2007 13. A random sample of 21 desktop PCs is selected. The mean life span is 6.8 years with a standard deviation of 2.4 years. Construct a 95% confidence interval for the mean life span of all desktop PCs. Assume that the life spans of all desktop PCs are approxi- mately normally distributed. (a) (6.85, 7.75) {b) (1.68, 3.12) ( (5.60, 8.00) AQ? (6.71, 7.89) (e) (5.77, 7.83) 14. Which of the following statements are true about the sampling distribution of £? * / I. The mean of the sampling distribution is equal to the mean of the population. . Ul. The shape of the sampling distribution is always approximately normal, when 7 “ is sufficiently large qa > 30). “3 (a) II only Swe {b) IE only {c) I and II only A@I 1 and 1 only. {e) None of above. STAT1222 page 6 of 13 May 3, 2007 15. A study of 4200 cell phone users found that 135 of them developed cancer of the brain or nervous system. Construct a 95% confidence interval of the proportion of cell phone users who develop cancer of the brain or nervous system. ——e (a) (0.0175 , 0.0225) , b)) (0.0267, 0.0375)” {c) (0.190, 0.214) (d) (495 ,209) (e) (0.75, .85) 2 PES CPG ye, 16, The following table gives the probability distribution of the number of girls in the families of four children. Number of Girls 0 po =0.23, ¢ =1.23 } pe =0.65, o =0.786 ‘(c) 2 =2.00, « =1.937 1. (d) 4 =2.35, o =0.521 Gow Ss (e) =3.45, o =0.281. STAT 1222 page 7 of 13 May 3, 2007 The following is used for questions 17, 18 and 19. ‘The following data gives the brain volumes for a group of patients with obsessive-compulsive disorders and a control group of healthy persons. Assume that the distributions of the andard brain volumes for these two groups of people are approximately normal with equal deviation. Control group | Patients my =10 ny = 10 #, = 0.45 Zy = 0.34 8; = 0.08 $2 = 0.07 At 0.01 significant level, test the claim that the means of the brain volumes for these two ‘i i 17. Choose the correct hypotheses to test the claim. (a) Ho: pa > pa versus Hy: tn < po 2 (b) Ho: &; > fq versus Hy: % < Fe (c)_ Ho: fy S fe versus Hy : py > fe nC (e) Ho: pa < pg versus Ha : jy > pa iN SS 18. Find the value of the standardized test statistic. (a) 0.62 (b) 1.85 \ (c),, 2.27 ‘ P(g)’ 3.27 “Y(e) 3.53 19. Find the critical value for the test and state your conclusion at a = .01. (a) The critical value is 2.861. The decision: Accept Ho . The critical value is 2.552. The decision: Reject Ho The critical value is 2.878. The decision: Reject Hp (d) The critical value is 2.539. The decision: Accept Ho : Reject Ho STAT1222 page 10 of 13 May 3, 2007 The following is used for questions 25. The following table gives the car weight,x (in lb) and the fuel consumption, y (in miles/gal) for 7 randomly selected cars. Weight | 3175 3450 3225 3985 2440 2500 2290 MPG | 27 29 27 24 37 34 37 The regression equation is 9 = —0.00797z + 54.7. 25. Predict the fuel consumption in MPG if the car weight is x = 3000 lb. (a) The MPG is 25.16 (b) The MPG is 28.51 i) The MPG is 30,79 (d) The MPG is 35.22 a (e) The MPG cannot be predicted ~ End of Multiple Choice Section STAT1222 page 11 of 13 May 3, 2007 1. 10 people were randomly selected, and their systolic (x) and diastolic (y) blood pressures were measured. 2° Systolic |. 138 130 185 140 120 125 120 130 130 144 Diastolic | 82 91 100 100 80° 90 80 80 80 .98 From the data, we have: Se=1312, Soe? = 172730, Sly =88l, Soy? = 78309, Say = 116008. {a). (6 pts.) Calculate the correlation coefficient, r, between the systolic and dias- tolic blood pressures.» (c). 6 pts.) “Use the equation in part (c) to predict y when x = 128. wy STAT1222 page 12 of 13 May 3, 2007 2. The following is the list of the ages of 12 Oscar-winning Actresses. 20 24 27 39 338 29 29 38 42 74 27 28 (a) (4pts.) Find the five number summaries Quartile, Third Quartile, Maximum). e., (Minin i w Fase er | Ze (b) (4 pts.) Find the inter-quartile range. Phy