Question

Suppose you have a process with two clerks, and want to determine whether they are processing the bills with a similar error rate. You sample the bills that they process, and find the following.

Clerk 1: N=236 bills, 5 mistakes

Clerk 2: N=202 bills, 8 mistakes

Based on a proportions test, which of the following could you conclude, and with what associated p-value?

A) there is no difference between clerks, p-value 0.87

B) there is no difference between clerks, p-value 0.26

C) there is a difference between clerks, p-value 0.05

D) there is a difference between clerks, p-value 0.02

Answer 1

Here

sample proportion of error rate for clerk 1 =  

sample size of bills done by clerk 1 = n₁ = 236

sample proportion of error rate for clerk 2 =  

sample size of bills done by clerk 2 = n₂ = 202

To test against

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value Since P-value = 0.267744 > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that :

B) there is no difference between clerks, p-value 0.26 (ans)