An extensive study of the cost of health care in the United States presented dat

Question

An extensive study of the cost of health care in the United States presented data showing that the mean spending perMedicareenrollee in 2003 was $6,883 (Money, Fall 2003). To investigate differences across the country, a researcher took a sample of 40 Medicare enrollees in Indianapolis. For the Indianapolis sample, the mean 2003 Medicare spending was $5,980 and the standard deviation was $2,498.

a. State the hypotheses that should be used if we would like to determine whether the mean annual Medicare spending in Indianapolis is lower than the national mean.

b. Use the preceding sample results to compute the test statistic and thep-value.

Test statistic (to 2 decimals)

Using?= .05, what is the critical value for the test statistic (to 3 decimals)?

Explanation / Answer

A) H0: Mean annual Medicare spending in Indianapolis is the same as the national mean (for 2003). HA: Mean annual Medicare spending in Indianapolis is lower than the national mean (for 2003). B) H0: µ = 6883 HA: µ < 6883 Sample mean = 5980 Standard deviation = 2518 Standard error of mean = s / v n Standard error of mean = 2518 / v 40 SE = 2518/6.3246 Standard error of mean 398.1308 t = (xbar- µ ) / SE t = (5980-6883) / 398.1308 t = -2.2681 p-value =0.014 Therefore p-value

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