A billing company that collects bills for doctors\' offices in the area is conce
ID: 3062563 • Letter: A
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 8,975 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.) Complete parts a through e below.
1. Write the appropriate hypotheses. Let p be the proportion of bills being paid by medical insurance. Choose the correct answer below.
2. Perform the test and find the P-value. What is the test statistic?
3. What is the P-value?
4. State your conclusion.
5. Do you think this difference is meaningful?
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.33
Alternative hypothesis: P 0.33
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).
= sqrt[ P * ( 1 - P ) / n ]
= 0.00496
z = (p - P) /
z = 2.02
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability that the z-score is less than -2.02 or greater than 2.02.
Thus, the P-value = 0.0434
Interpret results. Since the P-value (0.0434) is less than the significance level (0.05), we have to reject the null hypothesis.
From the above test we have sufficient evidence of a change in the percent of bills being paid by medical insurance.
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