Once the affordable care act was was instituted, there has been a debate about i

Question

Once the affordable care act was was instituted, there has been a debate about its affect on hospital costs. The senator that you are doing an internship for claims that it has resulted in the mean daily cost being more than 1,500 per day. You take a random sample of the daily cost of 289 community hospitals and find a mean daily cost of $1323. The population standard deviation for daily cost is known to be $50. Test the senators claim that the mean cost is higher than $1500 at a .10 significance level . State hypothesis show claim Once the affordable care act was was instituted, there has been a debate about its affect on hospital costs. The senator that you are doing an internship for claims that it has resulted in the mean daily cost being more than 1,500 per day. You take a random sample of the daily cost of 289 community hospitals and find a mean daily cost of $1323. The population standard deviation for daily cost is known to be $50. Test the senators claim that the mean cost is higher than $1500 at a .10 significance level . State hypothesis show claim

Explanation / Answer

Given that,
population mean(u)=1500
standard deviation, =50
sample mean, x =1323
number (n)=289
null, Ho: =1500
alternate, H1: !=1500
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
since our test is two-tailed
reject Ho, if zo < -1.645 OR if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 1323-1500/(50/sqrt(289)
zo = -60.18
| zo | = 60.18
critical value
the value of |z | at los 10% is 1.645
we got |zo| =60.18 & | z | = 1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -60.18 ) = 0
hence value of p0.1 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: =1500
alternate, H1: !=1500
test statistic: -60.18
critical value: -1.645 , 1.645
decision: reject Ho
p-value: 0

we have enough evidence to support the claim

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