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.

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