Answer:
Zstatistic < Zcritical ; then we reject the null
-0. 790 > - 1.96
Hence, we fail to reject the Null
Explanation:
Define the null and alternative hypothesis :
H0 : μ = 421
H1 : μ < 421
Given that :
Sample mean (x) = 416
Sample standard deviation, s = 29
α = 0.025
Sample size, n = 21
This is a lef tailed teast, hence if ;
Decision Rule :
Zstatistic < Zcritical ; then we reject the null
Zcritical at α = 0.025 (1 tailed) = - 1.96
Zstatistic = (x - μ) s/sqrt(n)
(416 - 421) / 29/sqrt(21)
Zstatistic = - 5 / 6.3283188
Zstatistic = - 5 / 6.3283188 = - 0.79
-0. 79 > - 1.96
Hence, we fail to reject the Null