Question

A billing company that collects bills for doctors' offices in the area is concerned that the percentage of bills being paid by medical insurance has risen. Historically, that percentage has been 33%. An examination of 9,378 recent, randomly selected bills reveals that 34% of these bills are being paid by medical insurance. Is there evidence of a change in the percent of bills being paid by medical insurance? (Consider a P-value of around 5% to represent reasonable evidence.)

Perform the test and find the P-value. What is the test statistic?

(Round to two decimal places as needed.)

Answer 1

Let p denote the current population percentage of bills paid by medical insurance.

We are testing :

H₀ : p = 0.33

H₁ : p 0.33

Now, Under H₀ :

where

is the sample proportion.

p is the value of the population proportion under H₀.

n is the sample size.

Now, we are given that :

Thus, the value of the test-statistic is :

Since, the test is two tailed, the p-value of the test statistic is:

Since, the p-value is less than 0.05 we can reject H₀ : p = 0.33 at 5% level of significance and conclude that p 0.33, i.e., percent of bills paid by medical insurance have changed.