MS Module 8 Confidence interval for difference in proportions practice exam questions

(The attached PDF file has better formatting.)

The observations and successes for a treatment group and a control group are

    treatment    control
observations    80    101
successes    56    67


The difference in the probability of success is the probability of success for the treatment group minus the probability of success for the control group.


Question 8.1: Sample difference in the probability of success

What is the sample difference in the probability of success between the two groups?

Answer 8.1: 56 / 80 – 67 / 101 = 0.0366


Question 8.2: Variance of the difference

What is the sample variance of the difference in the probability of success between the two groups?

Answer 8.2: (56 / 80 × (1 – 56 / 80) ) / 80 + (67 / 101 × (1 – 67 / 101) ) / 101 = 0.004836


Question 8.3: Standard deviation of the difference

What is the sample standard deviation of the difference in the probability of success between the two groups?

Answer 8.3: 0.0048360.5 = 0.0695


Question 8.4: z value for confidence interval

What is the z value for the 90% two-sided confidence interval for the difference in the probability of success for the two groups?

Answer 8.4: 1.645

(the z value for the 90% two-sided confidence interval is the z value for the 95% one-sided test)


Question 8.5: Upper bound of confidence interval

What is the 90% two-sided confidence interval for the difference in the probability of success for the two groups?

A.    0.0446
B.    0.0428
C.    0.1258
D.    0.1510
E.    0.2654

Answer 8.5: 0.0366 ± 1.645 × 0.0695

●    lower bound: 0.0366 – 1.645 × 0.0695 = -0.0777
●    upper bound: 0.0366 + 1.645 × 0.0695 = 0.1509

In Question 8.2: Why we are not using the formula (10.3) in the book pag. 519?

For a large sample test procedure of proportions when the null hypothesis assumes the probability of success is the same, we use equation 10.4 on page 520.