Exam I Solutions, Ma442,Spr04 - ijuflopJ Exam 1‘[VI/Mm...

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Unformatted text preview: ijuflopJ Exam 1‘ [VI/Mm ff?— 1. (28 pts.) Critical Region Hypothesis Test: Consider tanding a 1962 penny on edge on a hard smooth surface, spinning it, and then waiting for it to land on a side. Your instructor actually conducted 50 such spinnings of a 1962 penny and obtaind 43 tails in 50 tria s t eallyl). A fellow statistical educator claims that tails comes up 90% of the time. Do you believe him? —~———-—_— Conduct the appropriate hypothesis test below (with a = 0.05): P 2 F( T a. Hypotheses - state the null and alternative hypotheses: Ho: P270 HA1 Fifiv b. Decision Rule - tell me for what values of Z we accept the null and for what values of Z we reject the null (feel free to draw a picture): male; n I: In amt) .1 H.) (I: ma, 4)..“ J 1 ’9‘? ?"o7 f§ 4,9er 544 MrW-vq c. Computed Value of Z: A 22L. .5’ -. ‘i _ 4 ~ .‘7 “MK-V fiflgy “ .___. d. Conclusion: {0 (Fr-on Vlfibha-s M mwr) MM 14, e. What condition on n allows you to trust the normality of the Z statistic (for full-credit, state the condition given most recently in class rather than the condition for using the CLT from Math 441): WV,n(l-—p)a(° ex) 1 517564454 V0“ $191k l0?" "(l—‘3) H7610; Sal/I“ m 2. (16 pts.) Individuals in my Engineering Statistics 11 class Spring 2001 played the dice game ‘Drop Dead’ 16 times obtaining the scores: 9, 2, 4, 0, 9, 35, 5, 27, 21, 67,11, 9, 24,16, 30, 47 For these 16 numbers we have an average of A7 = 19.75 with a standard deviation of s 518.24. a. Give the standard point estimate for the true mean score1 y for an individual in the game Drop Dead. M?Z9|7«75 b. Give a 95% confidence interval for the true mean score y for an individual in the game Drop Dead. {it 2.15: if 2' 00.033, 21%?) 4:: j/‘szL fifimruz/ yup n 05¢; A k Cum/E. (J£;/4-/=/;) c. What did you assume about the population of Drop Dead scores in your calculation in part b (circle one of the following responses)? I in flhffl’: i. Nothin ii. Dro - ead scores follow some normal distributio iii. Drop Dead scores follow some t o istn ution / iv. Drop Dead scores follow some 12 distribution 1 Johnson, R. (1996), “The dice game ‘drop dead’", Teaching Mathematics & Its Applications, vol. 15, no. 3, pp. 97-98, actually shows how [.1 may be computed exactly. 3. (28 pts.) p-value Hypothesis Test: The production of a nationally marketed detergent results in certain workers receiving prolonged exposure to Bacillus subtilis enzyme. Nineteen workers were tested2 to determine the effects of this exposure. In particular, a measure of airflow rate3 was computed for each worker. Suppose that if the enzyme has an effect that this will result in a reduction in the airflow rate. M Here are thata values (of airflow rate) sorted from smallest to largest: 0.61 0.63 0.64 0.67 0.70 0.72 0.73 0.74 0.76 0.78 0.82 0.82 0.82 0.83 0.84 0.85 0.85 0.87 0 88 For these data the sample average ififijfihfigd the sample standard deviafion®fi .5 Suppose that in persons with no lung dysfunction that the mean airflow rate is 0.80. Conduct a test to see whether workers exposed to the Bacillus subtilis enzyme have, on average, a reduced airflow rate. Conduct the appropriate hypothesis test below ( ' I a. State the null and alternative hypotheses. H D : A ¢ . 7 0 HP, : M < . X D b. The statistic that you compute in this roblem has, depending possibly upon assumptions made, either an approximate normal density or ell me which one — normal or t. If you say t then also give me the degrees of freedom. /£,¢L%;+y JF:V\’I=[7*I:IX 0. Compute the test statistic (the z— or t—value) ’n. ’E z ’1‘ “ 0 yo 1: ' 5m : pew/fl? d. Draw a picture shading the area that is equal to the p—value. Be sure to label any relevant value(s) along the horizontal axis. Compute, as best you can, the p-value using either an attached table or your calculator. «13,5, U 5M7 ‘l.’ «I’lbk \ W” (Alva W .05 < V"’“'”‘ <' ‘0 4““ [may V‘qlug wok clue.» «h» 0‘05) e. What is your conclusion? That is, are you going to accept or reject H0 ? [b purelw” 7 .05/ 4604A” Ho 2 Shore, Neil eta]. (1971), “Lung dysfunction in workers exposed to Bacillus subtilis enzyme", Environmental Research, vol. 4, pp. 512-519. 3 Technically, the ratio of a person’s forced expiratory volume in one-second to his/her vital capacity is computed. 4. (8 pts.) In question 3 we needed to assume what (choose one): ulation of airflow rates follows some normal distributlo iii. The population of airflow rates follows some ' ' iv. The population of airflow rates follows some 12 distribution 5. (8 pts.) In question 3 there are 19 data values. Suppose we want to check the normality of airflow rates by graphing the corresponding normal probability plot. i. —1.04 ii. 0.5596 iii. 0.64 iv. 0.7357 6. (12 pts.) Multiple Choice: a. Which of the following symbols may appear in a null (H a) or alternative (H A) hypothesis (circle those that can)? a [an x b. Which hypothesis alternative — necessarily has an = symbol (circle the correct response)? c. For the test Hozp=10 ’ HAzy>10 we will reject H0 when t or 2 (as the case may be) is . . . (choose one): c. big or small d. For the test Hazy=10 HA:,u¢lO we will reject H a when t or 2 (as the case may be) is . . . (choose one): a. big b. II o 1 . big or small ...
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