The US Agency for Healthcare Research and Quality reports th

The US Agency for Healthcare Research and Quality reports that in 2010, the mean cost of hospital stay for American woman aged 18 - 44 was $15,200. A random sample of 400 hospital stays of women 18 - 44 showed mean cost of $16,000 with a standard deviation o, $5000. Test whether the cost of hospital stays for the age group has increased since 2010 a level of significance of 0.05.

Solution

2.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   15200  
Ha:    u   >   15200  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    16000          
uo = hypothesized mean =    15200          
n = sample size =    400          
s = standard deviation =    5000          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.2          
              
Also, the p value is              
              
p =    0.000687138          
              
As z > 1.6449, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the cost of hospital stays for the age group 18-44 has increased since 2010 at 0.05 level. [CONCLUSION]