Question

2 of 2 ID: MST.FET.CP.ITPP.02.0020A [2 marks] A computer training group would like to compare the effectiveness of two modes of training. The first mode of training is a short 20 minute interactive one-on-one tutorial with the participant and the second mode is a one hour video that the participant watches. A random sample of 55 people are invited to take part in the tutorial, which is followed by a test to measure competency at the tasks covered. The number of people that pass this test is 24. Similarly, a random sample of 44 people are invited to watch the video, which is also followed by the same test. The number of people that pass this test is 20. Let "1 denote the population proportion of people that would pass the competency test after taking the tutorial. Similarly, let denote the population proportion of people that would pass the competency test after watching the video. Construct a 95% confidence interval for the difference between these two proportions (r1 - 12). Give your answers to 3 decimal places. You may find this standard normal table useful.

Answer 1

The sample Proportion for first mode of training is

The sample Proportion for second mode of training is

$\widehat{p}_{2} = \frac{Y}{n} = \frac{20}{44} =0.455$

95% CI for the difference between the two proportions is

R2

0.436 0.564 0.455 0.545 = (0.436-0.455) 1.96 --

$=-0.019\pm 0.197$

Answer: The 95% CI is  

-0.216 < π1--2ー0.178