In: Statistics and Probability
A random sample of 105 observations produced a sample mean of 33. Find the critical and observed values of z for the following test of hypothesis using α=0.025. The population standard deviation is known to be 9 and the population distribution is normal.
H0: μ=28 versus H1: μ>28.
Round your answers to two decimal places.
zcritical =
zobserved =
Solution :
This is the right tailed test,
The null and alternative hypothesis is ,
H0 :
= 28
Ha :
> 28
α = 0.025.
P(z > z ) = 0.025
= 1 - P(Z < z) = 0.025
= P(Z < z) = 1 - 0.025
= P(Z < z ) = 0.975
= P(Z < 1.96 ) = 0.975
z > 1.96
Test statistic = z =
= (
-
) /
/
n
= (33 - 28) / 9 /
105
Test statistic = z = 5.69