. The state's education secretary claims that the average cost of one year's tuition for all...

. The state's education secretary claims that the average cost of one year's tuition for all private high schools in the state is $2350.00.A sample of 35 private high schools is selected, and the average tuition is $2315.00. The population standard deviation is $38.00. At a significance level of 0.05, is there enough evidence to reject the claim that the average cost of tuition is equal to $2350.00?

Expert Solution

Given that,
population mean(u)=2350
standard deviation, σ =38
sample mean, x =2315
number (n)=35
null, Ho: μ=2350
alternate, H1: μ!=2350
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 2315-2350/(38/sqrt(35)
zo = -5.449
| zo | = 5.449
critical value
the value of |z α| at los 5% is 1.96
we got |zo| =5.449 & | z α | = 1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : two tailed ( double the one tail ) - ha : ( p != -5.449 ) = 0
hence value of p0.05 > 0, here we reject Ho
ANSWERS
---------------
null, Ho: μ=2350
alternate, H1: μ!=2350
test statistic: -5.449
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0
we have enough evidence to support the claim that the average cost of tuition is equal to $2350.00.

milcah answered 1 year ago

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