Consider the following hypotheses H0 126 HA 126 A sample of

Consider the following hypotheses:   H0: 12.6   HA: > 12.6

A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a known population standard deviation of 3.2 and that =0.10. We’re going to conduct this test using the p-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) What is the significance level? Under what conditions will we reject H₀?

3) Calculate the test statistic and p-value.

4) What is your conclusion?

Solution

Set Up Hypothesis
Null Hypothesis H0: U<=12.6
Alternate Hypothesis H1: U>12.6
Test Statistic
Population Mean(U)=12.6
Given That X(Mean)=13.4
Standard Deviation(S.D)=3.2
Number (n)=25
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=13.4-12.6/(3.2/Sqrt(25)
Zo =1.25
| Zo | =1.25
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =1.25 & | Z | =1.28
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value : Right Tail - Ha : ( P > 1.25 ) = 0.1056
Hence Value of P0.1 < 0.1056, Here We Do not Reject Ho

ANS:
RIGHT TAILED
The Value of |Z | at LOS 0.1% is 1.28, Reject Ho, when Z>1.28
Zo =1.25, Right Tail - Ha : ( P > 1.25 ) = 0.1056
Do not Reject Ho