Answer:
We conclude that the population mean cost for a hospital stay for American women aged 18-44 has increased since 2010.
Step-by-step explanation:
We are given that the US Agency for Healthcare Research and Quality reported that in 2010 the mean cost of a stay in a hospital for American women aged 18-44 was $15,200.
A random sample of 400 hospital stays for American women aged 18-44 showed a mean cost of $16,000, with a standard deviation of $5000.
<u><em>Let </em></u><u><em> = population mean cost for a hospital stay for American women aged 18-44.</em></u>
SO, <u>Null Hypothesis</u>, :
$15,200 {means that the population mean cost for a hospital stay for American women aged 18-44 has reduced or remains same since 2010}
<u>Alternate Hypothesis</u>, :
> $15,200 {means that the population mean cost for a hospital stay for American women aged 18-44 has increased since 2010}
The test statistics that will be used here is <u>One-sample t test</u> <u>statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean cost of a stay in a hospital for American women aged 18-44 = $16,000
s = sample standard deviation = $5,000
n = sample of hospital stays = 400
So, <em><u>test statistics</u></em> = ~
= 3.20
<em>Now at 5% significance level, the t table gives critical value of 1.645 at 399 degree of freedom for right-tailed test. Since our test statistics is more than the critical value of t as 1.645 < 3.20, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.</em>
Therefore, we conclude that the population mean cost for a hospital stay for American women aged 18-44 has increased since 2010.