Identify the null hypothesis alternative hypothesis test sta

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. 4) The health of employees is monitored by periodically weighing them in. A sample of 54 employees has a mean weight of 183.9 lb. Assuming that is known to be 121.2 lb, use a 0.10 significance level to test the claim that the population mean of all such employees weights is less than 200 lb.

Solution

Set Up Hypothesis
Null, H0: U=200
Alternate, H1: U<200
Test Statistic
Population Mean(U)=200
Given That X(Mean)=183.9
Standard Deviation(S.D)=121.2
Number (n)=54
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=183.9-200/(121.2/Sqrt(54)
Zo =-0.9762
| Zo | =0.9762
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =0.9762 & | Z | =1.28
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Left Tail - Ha : ( P < -0.9762 ) = 0.1645
Hence Value of P0.1 < 0.1645, Here We Do not Reject Ho

We don\'t have evvidence to support the population mean of all such employees weights
is less than 200 lb