A random sample of n 35 observations from a quantitative po

A random sample of n = 35 observations from a quantitative population produced a mean x = 2.4 and a standard deviation s = .29. Suppose your research objective is to show that the population mean mu exceeds 2.3. Give the null and alternative hypotheses for the test. Locate the rejection region for the test using a 5% significance level. Find the standard error of the mean. Before you conduct the test, use your intuition to decide whether the sample mean x = 2.4 is likely

Solution

Set Up Hypothesis
Null, H0: U=2.3
Alternate, H1: U>2.3
Test Statistic
Population Mean(U)=2.3
Sample X(Mean)=2.4
Standard Deviation(S.D)=0.29
Number (n)=35
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =2.4-2.3/(0.29/Sqrt(35))
to =2.04
| to | =2.04
Critical Value
The Value of |t | with n-1 = 34 d.f is 1.691
We got |to| =2.04 & | t | =1.691
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 2.04 ) = 0.02459
Hence Value of P0.05 > 0.02459,Here we Reject Ho

[ANSWERS]
1. H0: U=2.3 , H1: U>2.3
2. |t | with n-1 = 34 d.f is, Reject Ho if Zo> 1.691