Question

For a sample of 35 items from a population for which the standard deviation is 20.5, the sample mean is 458. At the 0.05 level of significance, test H0: µ = 450 verses H1: µ ≠ 450. Determine and interpret the p-value for the test.

Given the information in the previous question, construct a 95% confidence interval for the population mean, then reach a conclusion regarding whether µ could actually be equal to the value that has been hypothesized. How does this conclusion compare to that reached in the previous question? Why?

Answer 1

To Test :-

H0: µ = 450

H1: µ ≠ 450

Test Statistic :-

P value = P ( Z > 2.31 ) = 1 - P ( Z < 2.31 )

P ( Z > 2.31 ) = 1 - 0.98952 = 0.01048

Since alternative hypothesis is two tailed we need to multiply the probability by 2

P - value = 2 * 0.01048 = 0.02096

Test Criteria :-

Reject null hypothesis if P value < level of significance

P value = 0.02096 < 0.05, we reject null hypothesis

Conclusion :- Accept Alternative Hypothesis

µ ≠ 450

Confidence Interval

Lower Limit =

Upper Limit =

95% confidence interval is ( 451.285 , 464.7915 )

does not lie in the confidence interval

We can make the decision based on confidence interval

If   does not lie in the interval we reject null hypothesis OR accept otherwise.

Result :- Reject null hypothesis.