The Department of Managed Health Care in the State of California (USA) has adopt

Question

The Department of Managed Health Care in the State of California (USA) has adopted a number of regulations to ensure that managed care enrollees have access to healthcare services in a timely manner. One of these regulations requires that health care plans show that their provider networks are sufficiently large to ensure that enrollees be offered an appointment with a primary care provider within 10 business days of such a request. Suppose that you are an intern for a health insurer and that you have been asked to determine whether or not your company is in compliance with this regulation. Hypothetical data on a random sample of patients insured with your company are presented in Fig. 4.6: on your Excel spreadsheet, write the null hypothesis and the research hypothesis for these data. Use Excel to find the sample size, mean, standard deviation, and standard error of the mean for these data (two decimal places for the mean, standard deviation, and standard error of the mean). Use Excel to perform a t-test on these data (two decimal places). On your printout, type the critical value of t given in your t-table in Appendix E. On your spreadsheet, type the result of the t-test. On your spreadsheet, type the conclusion of your study in plain English. save the file as: DISCHARGE3

Explanation / Answer

(a) Ho: no of appointment days = 10 vs H1: no of appointment days > 10

(b) You can use excel to find out by directly using the formula, but here I am using R for this purpose as I am not allowed to upload spreadsheet here!

> ad=c(7,18,12,16,19,21,8,6,4,15,16,18,17,16,12,9,11,14,13)
> size=length(ad)
> round(mean(ad),2)
[1] 13.26
> round(sd(ad),2)
[1] 4.77
> se=sd(ad)/sqrt(size) #mean should be 10 in ideal case
> round(se,2)
[1] 1.09

In excel , you can use =COUNT, =AVERAGE,=STDEV.S,=STDEV.S/SQRT(N) etc.

(c)

> t.test(ad,alternative = "greater",mu=10)

   One Sample t-test

data: ad
t = 2.9814, df = 18, p-value = 0.004001
alternative hypothesis: true mean is greater than 10
95 percent confidence interval:
11.36524 Inf
sample estimates:
mean of x
13.26316

> qt(.95,18)
[1] 1.734064

So, tabulated t value is 1.73 and calculated value is 2.98

Hence we reject the null hypothesis and thus we may conclude that the company is not in compliance with the stated regulation

In excel, you can make use of

say, N=sample size then df=N-1 se=sd/sqrt(N) t_calc=(mean - 10)/se

and for t value tabulated use, =T.INV(.95,df)

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