Question

5. You have data on the quality scores of 25 hospitals in the state of Florida. The possible scores that hospitals can have are from 1 to 5, with 1 being the lowest and 5 the highest. The data show the following scores: 1.1, 1.3, 1.5, 1.8, 1.9, 2, 2.4, 2.5, 2.5, 2.8, 3.1, 3.1, 3.3, 3.6, 3.7, 3.7, 3.8, 3.9, 3.9, 3.9, 4, 4.2, 4.3, 4.4, 4.9. You want to compare these scores to the national average score of 3.3 with a standard deviation of 1.02 (Note that the Florida score is lower than the national average). Further, you want to statistically test whether the Florida scores are significantly lower than the national average (alternative hypothesis). Your null hypothesis is that the Florida scores are not lower. Can you reject your null hypothesis (and support your alternative hypothesis?) Test your null hypothesis at a p value of 0.05. Note that this question builds on results from questions #1, 2, 3, & 4.

Yes.

No.

cannot be determined from the information given.

Answer 1

H0: Null Hypothesis:

HA: Alternative Hypothesis

SE =

From the given data, the sample mean is calculated as follows:

Table of Area Under Standard Normal Curve gives area = 0.3315

So,

P-Value = 0.5 - 0.3315 = 0.1685

Since P-Value= 0.1685 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that the Florida scores are significantly lower than national avrage score.

The data do not support the claim that the Florida scores are significantly lower than national avrage score.