# ch8 - Chapter 8 Tests of Statistical Hypotheses 8.1 Tests...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 8 Tests of Statistical Hypotheses 8.1 Tests about Proportions 8.1–2 (a) C = { x : x = 0 , 1 , 2 } ; (b) α = P ( X = 0 , 1 , 2; p = 0 . 6) = (0 . 4) 4 + 4(0 . 6)(0 . 4) 3 + 6(0 . 6) 2 (0 . 4) 2 = 0 . 5248; β = P ( X = 3 , 4; p = 0 . 4) = 4(0 . 4) 3 (0 . 6) + (0 . 4) 4 = 0 . 1792 . OR (a ) C = { x : x = 0 , 1 } ; (b ) α = P ( X = 0 , 1; p = 0 . 6) = (0 . 4) 4 + 4(0 . 6)(0 . 4) 3 = 0 . 1792; β = P ( X = 2 , 3 , 4; p = 0 . 4) = 6(0 . 4) 2 (0 . 6) 2 + 4(0 . 4) 3 (0 . 6) + (0 . 4) 4 = 0 . 5248 . 8.1–4 Using Table II in the Appendix, (a) α = P ( Y ≥ 13; p = 0 . 40) = 1- . 8462 = 0 . 1538; (b) β = P ( Y ≤ 12; p = 0 . 60) = P (25- Y ≥ 25- 12) where 25- Y is b (25 , . 40) = 1- . 8462 = 0 . 1538 . 8.1–6 (a) z = y/n- 1 / 6 p (1 / 6)(5 / 6) /n ≤ - 1 . 645; (b) z = 1265 / 8000- 1 / 6 p (1 / 6)(5 / 6) / 8000 =- 2 . 05 <- 1 . 645, reject H . (c) [0 , b p + 1 . 645 p b p (1- b p ) / 8000] = [0 , . 1648], 1 / 6 = 0 . 1667 is not in this interval. This is consistent with the conclusion to reject H . 8.1–8 The value of the test statistic is z = . 70- . 75 p (0 . 75)(0 . 25) / 390 =- 2 . 280 . (a) Since z =- 2 . 280 <- 1 . 645, reject H . (b) Since z =- 2 . 280 >- 2 . 326, do not reject H . (c) p-value ≈ P ( Z ≤ - 2 . 280) = 0 . 0113. Note that 0 . 01 < p-value < . 05. 109 110 Chapter 8 8.1–10 (a) H : p = 0 . 14; H 1 : p > . 14; (b) C = { z : z ≥ 2 . 326 } where z = y/n- . 14 p (0 . 14)(0 . 86) /n ; (c) z = 104 / 590- . 14 p (0 . 14)(0 . 86) / 590 = 2 . 539 > 2 . 326 so H is rejected and conclude that the campaign was successful. 8.1–12 (a) z = y/n- . 65 p (0 . 65)(0 . 35) /n ≥ 1 . 96; (b) z = 414 / 600- . 65 p (0 . 65)(0 . 35) / 600 = 2 . 054 > 1 . 96, reject H at α = 0 . 025. (c) Since the p-value ≈ P ( Z ≥ 2 . 054) = 0 . 0200 < . 0250, reject H at an α = 0 . 025 significance level; (d) A 95% one-sided confidence interval for p is [0 . 69- 1 . 645 p (0 . 69)(0 . 31) / 600 , 1] = [0 . 659 , 1] . 8.1–14 We shall test H : p = 0 . 20 against H 1 : p < . 20. With a sample size of 15, if the critical region is C = { x : x ≤ 1 } , the significance level is α = 0 . 1671. Because x = 2, Dr. X has not demonstrated significant improvement with these few data. 8.1–16 (a) | z | = | b p- . 20 | p (0 . 20)(0 . 80) /n ≥ 1 . 96; (b) Only 5/54 for which z =- 1 . 973 leads to rejection of H , so 5% reject H . (c) 5%. (d) 95%. (e) z = 219 / 1124- . 20 p (0 . 20)(0 . 80) / 1124 =- . 43, so fail to reject H . 8.1–18 (a) Under H , b p = (351 + 41) / 800 = 0 . 49; | z | = | 351 / 605- 41 / 195 | s (0 . 49)(0 . 51) 1 605 + 1 195 = | . 580- . 210 | . 0412 = 8 . 99 . Since 8 . 99 > 1 . 96, reject H . (b) . 58- . 21 ± 1 . 96 r (0 . 58)(0 . 42) 605 + (0 . 21)(0 . 79) 195 . 37 ± 1 . 96 √ . 000403 + 0 . 000851 . 37 ± . 07 or [0 . 30 , . 44] ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 24

ch8 - Chapter 8 Tests of Statistical Hypotheses 8.1 Tests...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online