Question

at alpha = 0.05, test to see if the true mean of the distribution from which the data was created is greater than 27.

sample mean = 29.875

Variance = 64.109378

Pop size = 16

Answer 1

From the above information,

We perform one sample z test

) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μ=27. v/s

Ha:μ>27

(2) Rejection Region

The rejection region for this right-tailed test is R={z:z>1.64} at alpha=0.05. Since c=1.64

(3) Test Statistics

The z-statistic is computed as follows:

z = (xbar-mu)/(sigma/sqrt(n)) =0.19

(4) Decision about the null hypothesis

Since it is observed that z=0.19<c=1.64, it is then concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is greater than 27, at the 0.05 significance level.

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