a Calculate the observed Zscore associated with the observed

a.) Calculate the observed Z-score associated with the observed outcome xbar=14 for a sample size of 16. Would this outcome lead to a rejection of Ho at the .05 level? At the .025 level? At the .005 level? Discuss the value of this test in light of your findings here.

Solution

Set Up Hypothesis
Null Hypothesis H0: U=10
Alternate Hypothesis H1: U!=10
Test Statistic
Population Mean(U)=10
Given That X(Mean)=14
Standard Deviation(S.D)=6
Number (n)=16
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=14-10/(6/Sqrt(16)
Zo =2.6667
| Zo | =2.6667

a.)
Zo =2.6667

AT 0.05, 0.025,0.005 critical choice given are 1.68, 1.96, and 2.58
We got |Zo| =2.6667 > | Z | in every case above
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho

b.)
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 2.6667 ) = 0.0077
Hence Value of P0.05 > 0.0077,Yes it is strongly Reject Ho