Z F a c t o r f o r 1 T a i l T e s t s = N O R M S I N V ( 0 . 0 1 ) * 1 = N O R M S I N V ( 0 . 0 2 ) * 1 = N O R M S I N V ( 0 . 0 4 ) * 1 = N O R M S I N V ( 0 . 0 5 ) * 1 = N O R M S I N V ( 0 . 1 ) * 1 = N O R M S I N V ( 0 . 1 5 ) * 1 = N O R M S I N V ( 0 . 2 ) * 1 Left Tail: F 1 - /2, n 2 -1, n 1 -1 Right Tail: F /2, n1 -1, n 2 -1 2-Tail Left (Lower) Tail 2-Tail Right (Upper) Tail F1-/2, n2 -1, n1-1 F-Factor Excel Syntax F/2, n1 -1, n2-1 F-Factor Excel Syntax F.975,11,9 0.2787 =FINV(0.975,11,9) F.025,9,11 3.5879 =FINV(0.02 BMRT 21004 Module 17 HW (20 Points) 4 Pages HW Problem 46. (5 pts) Is there a difference in the insurance costs employers pay for their managers and their professional specialty workers? The Bureau of Labor Statistics (BLS) wants to study this question. They randomly sample 35 managers which results in a sample mean cost of $1.84 per worker per hour with a sample standard deviation of $.38. They also randomly sample 41 professional specialty workers resulting in a sample mean cost of $1.99 with a standard deviation of $.51. At the .02 level of significance, test to determine if there's a difference in the hourly rates employers pay for insurance for their managers and their professional specialty workers? List and clearly label all eight steps. Step 1. H0 : 1 = u2 Ha: 1 u2 ( XX 1 - XX 2 ) - ( 1 - u 1) s21 s22 + n1 n2 Step 2. Z= Step 3. a=.02 Step 4. Reject the Null Hypothesis if Z < -2.3263 or if Z > 2.3263 Step 5. Population 1 (managers) n1 = 35, XX 1 =$1.84, s1 =$.38 Population 2 (specialty workers) n2= 41, XX2 = $1.99, s2= $.51 ( XX 1 - XX 2) - ( 1 - u 1 ) Step 6. Z= 2 1 2 2 s s + n1 n2 = (1.84 - 1.99 ) - (0) ( .38 ) 2 (.51 ) 2 + 35 41 Step 7. -1.4660 IS NOT LESS THAN -2.3263 we fail to reject the Null Hypothesis. = -1.4660 [ -1.4660 >- 2.3263] Therefore Step 8. At the .02 level of significance, there is enough evidence to conclude that average salaries for managers and specialty workers are different. HW Problem 47. (5 pts) A researcher wants to determine if the children of parents with college degrees perform better on the AP Calculus BC test than the children of parents who do not have college degrees. 18 high school students whose parents have college degrees are randomly sampled resulting in a sample mean score of 3.4 with a sample standard deviation of .4. 21 students whose parents are not collegeeducated are also randomly sampled, resulting in a sample mean AP score on the Calculus BC test of 3.0 with a sample standard deviation of .5. At the .05 level of significance, is there enough evidence to conclude that the children of parents with college degrees perform better on the AP Calculus BC test than the children of parents who do not have college degrees? List and clearly label all eight steps. Probably using t test. Could be wrong ( XX 1 - XX 2 ) - ( 1 - m 1 ) t= s 21 ( n 11 )+ s 22( n 21) 1 1 + n 1+n 22 n1 n2 HW Problem 48. (5 pts) Do a greater proportion of Kentucky residents than West Virginia residents enjoy possum stew? That's the momentous question being explored by a researcher with way too much time on his hands. The researcher randomly samples 320 residents from Kentucky and 176 express with an affinity for possum stew. Additionally, in a random sample of 280 West Virginians, 140 indicate they have a taste for possum stew. At the .01 level of significance, is there enough statistical evidence to conclude that the researcher is correct in his belief that a greater proportion of Kentucky residents than West Virginia residents enjoy possum stew? List and clearly label all eight steps. ( ^p 1 - ^p 2 ) ( P1 - P2 ) Z= Q 1 + 1 P n 1 n2 ( ) HW Problem 49. (5 pts) According to the U.S. General Accounting Office (GAO), the average age of a male government worker is 43.6 years and that of a male worker in the private sector is 37.3 years. Suppose a random sample of 15 male federal workers resulted in a sample standard deviation of 9.6 years and a random sample of 13 private sector male workers resulted in a sample standard deviation of 8.2 years. At the .01 level of significance, test to see if the variance of ages for male government workers is different than the variance of ages of male workers in the private sector. List and clearly label all eight steps. 2-Tail test: For a 2-tail test, we must determine 2 different F - factors: A left tail and a right tail. F 1 - /2, n 2 -1, n 1 -1 Left Tail: Right Tail: F /2, n1 -1, n 2 -1 1-Tail test: F 1 - , n 2 -1, n1 -1 1 Tail (Left) Test: F , n 1 -1, n 2 -1 1 Tail (Right) Test: As with the 2-tests for single population variances in Module 15, there is no negative numbers with an F-Test. Variances can't be negative. 2 S1 F = S2 2