Answer Happy

Question 2: Estimation and Hypothesis Tests-Two Populations. Part I. (15 Marks) In a survey, two independent random samples of workers of sizes m= 124 and n= 130 from two construction firms, were asked if they wear security helmets all the time. In the first sample 106 said yes, while in the second 98 said yes. Let p1 and p2 be the population proportions of workers of the two firms who wear their security helmets all the time. 1. Test the equality of p1 and p2 at a=0.05 (large sample procedure), by the same 5 steps as before. (10 Marks) 2. Construct a large sample 90% confidence interval for P1 – P2. (5 Marks) + Part II. (15 Marks) The following data is on the completion time of a machining task taken by a random sample of 12 trainees and a random sample of 15 professional machinists (independent samples): Completion times (in minutes) Trainees (X) 32 43 27 43 41 37 17 38 41 45 45 35 Professional 26 21 32 27 32 | 22 | 28 | 21 30 40 | 24 28 32 machinists (Y) Let Hy and uy be the corresponding population mean completion times, and assume that the populations from which these completion times were sampled are normally distributed. 1. Are the professional machinists faster on the average than the trainees ( MHz) at the 1% level of significance? Test this by the same 5 steps as before. (10 Marks) 2. Construct a 99% confidence interval for My-12. (5 Marks) 26 21 32 $ 21 30 40 24