According to the National Coalition on Health Care, the mean annual premium for an employer health...

According to the National Coalition on Health Care, the mean annual premium for an employer health plan covering a family of four cost $11,500 in 2007. A random sample of 100 families of four taken this year showed a mean annual premium of $11,750. Assuming  = $1500 , test whether the mean annual premium has increased, using a 0.05 significant level. Use the p-value method.

Expert Solution

Given that,
population mean(u)=11500
standard deviation, σ =1500
sample mean, x =11750
number (n)=100
null, Ho: μ=11500
alternate, H1: μ>11500
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 11750-11500/(1500/sqrt(100)
zo = 1.667
| zo | = 1.667
critical value
the value of |z α| at los 5% is 1.645
we got |zo| =1.667 & | z α | = 1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : right tail - ha : ( p > 1.667 ) = 0.048
hence value of p0.05 > 0.048, here we reject Ho
ANSWERS
---------------
null, Ho: μ=11500
alternate, H1: μ>11500
test statistic: 1.667
critical value: 1.645
decision: reject Ho
p-value: 0.048
we have enough evidence to support the claim that whether the mean annual premium has increased.

orchestra answered 2 years ago

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