The number of days between filing a health insurance claim and receiving payment

Question

The number of days between filing a health insurance claim and receiving payment (turnaround time) from U.S. insurance companies is known to be 26 days. In order to better serve its providers, company A has decided to pilot a new billing and coding system that is supposed to provide payments faster by reducing paperwork. Company A convinces 12 providers to try the new system and receives the following data on number of days from billing to payment: 26, 27, 27, 26, 25, 26, 18, 23, 28, 24, 26, 27. Do these data provide evidence of a significant decrease in turnaround time? Run the appropriate hypothesis test. Assume = 0.05. (9pts)

What type of hypothesis test is appropriate in this instance? Circle your answer and then carry out the hypothesis testing steps using the correct procedure:

One-sample z- test                 One-Sample t-test                  Paired sample t-test

      1) Hypotheses

                        Ho: Ha:

      2) Test Statistic

3) P-Value:

4) Conclusion

Generate a 95% confidence interval for the population mean (µ0) turnaround time. (3pts)

Explanation / Answer

Here one sample t - test is employed for hypothesis testing.

(1) H0 : = 26

Ha : < 26

(2) Here,

sample mean x = 25.25

Standard deviation of sample s = 2.667

standard error of sample mean se0 = s/sqrt(n) = 2.667/sqrt(12) = 0.77

Test statistic

t = (x - 26)/se0 = (25.25 - 26)/0.77 = -0.974

(3) P - value = TDIST (-0.974; 11) = 0.1755 > 0.05

(4) Here we failed to reject the null hypothesis and can conclude that there  data doesn't provide evidence of a significant decrease in turnaround time.

95% confidence interval = x +- t11,0.05 se0 = 25.25 +- 2.2 * 0.77 = (23.555,26.945)

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