Question

Once the Affordable Care Act was instituted, a debate began about its effect on hospital costs. The daily mean cost per day was $2,500 before the Act with a population standard deviation of $75. The nonprofit you work for claims that the Act resulted in the mean daily cost being less than $2,500 per day. You take a random sample of the daily costs of 25 community hospitals and find a mean daily cost of $2,470. Test the claim that the mean cost is lower than $2,500 at the .01 significance level. Be sure to show me the claim and the hypothesis as well as the values you are using to make your decision. What do you conclude about the hypothesis

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 2500

For the alternative hypothesis,

µ < 2500

This is a left tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 2500

x = 2470

σ = 75

n = 25

z = (2470 - 2500)/(75/√25) = - 2

Since it is a left tailed test, we would determine the area to the left of z = - 2 from the normal distribution table. the probability corresponding to the z score is 0.023

Since alpha, 0.01 < the p value, 0.023, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, there is not enough evidence that the mean cost is lower than $2,500