Consider the following hypotheses H0 150 HA 150 A sample of

Consider the following hypotheses: H0: 150 HA: < 150

A sample of 80 observations yields a sample mean of 144. The population standard deviation is known to be 28. We’re going to conduct this test using the critical value approach.

1) The hypotheses have already been given to you, but tell me what type of test this is: left-tailed, right-tailed, or two-tailed?

2) The significance level is =0.05. Calculate the critical value(s). Under what conditions will we reject H₀?

3) Calculate the test statistic.

4) What is your conclusion with respect to H₀

Solution

Set Up Hypothesis
Null Hypothesis H0: U>=150
Alternate Hypothesis H1: U<150
Test Statistic
Population Mean(U)=150
Given That X(Mean)=144
Standard Deviation(S.D)=28
Number (n)=80
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=144-150/(28/Sqrt(80)
Zo =-1.9166
| Zo | =1.9166
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.9166 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Left Tail - Ha : ( P < -1.9166 ) = 0.0276
Hence Value of P0.05 > 0.0276, Here we Reject Ho

ANS:
LEFT TAILED
The Value of Z at LOS 0.05% is <-1.64, We Reject Ho
Zo =-1.9166
Reject Ho