Question

Healthcare administration leaders are asked to make evidence-based decisions on a daily basis. Sometimes, these decisions involve high levels of uncertainty, as you have examined previously. Other times, there are data upon which evidence-based analysis might be conducted. This week, you will be asked to think of scenarios where building and interpreting confidence intervals (CIs) would be useful for healthcare administration leaders to conduct a two-sided hypothesis test using fictitious data. For example, Ralph is a healthcare administration leader who is interested in evaluating whether the mean patient satisfaction scores for his hospital are significantly different from 87 at the .05 level. He gathers a sample of 100 observations and finds that the sample mean is 83 and the standard deviation is 5. Using a t-distribution, he generates a two-sided confidence interval (CI) of 83 +/- 1.984217 *5/sqrt(100). The 95% CI is then (82.007, 83.992). If repeated intervals were conducted identically, 95% should contain the population mean. The two-sided hypothesis test can be formulated and tested just with this interval. Ho: Mu = 87, Ha: Mu<>87. Alpha = .05. If he assumes normality and that population standard deviation is unknown, he selects the t-distribution. After constructing a 95% CI, he notes that 87 is not in the interval, so he can reject the null hypothesis that the mean satisfaction rates are 87. In fact, he has an evidence-based analysis to suggest that the mean satisfaction rates are not equal to (less than) 87.

Given the information provided, complete the chart....

Null Hypothesis
Alternative Hypothesis
Sample size
Sample mean
Standard deviation
Standard error
t-value test statistic
Degrees of freedom
p-value
Reject %
Reject %
Reject %
Lower Limit of % CI
Upper Limit of % CI

Answer 1

The given chart is completed as follows:

Null Hypothesis	H0: = 87
Alternative Hypothesis	HA: 87
Sample Size	n = 100
Sample mean	= 83
Standard Deviation	s = 5
Standard error
t - value test statistic
Degrees of freedom	n - 1 = 100 - 1 =99
p - value	< 0.00001
Reject %	Difference is significant
Reject %	Reject null hypothesis
Reject %	Mean satisfaction rate is different from 87
Lower limit of % CI	82.007
Upper limit of % CI	83.992