Question

For the following hypothesis test:

?0: ? = 0.40

? A  : ? ≠ 0.40

? = 0.01

with n = 64 and p = 0.42

1. Find the critical value ??.
2. Calculate the value of the test statistic Z.
3. Test the hypothesis using the Z-Test Statistic and write your conclusion (decision).

Answer 1

For the following hypothesis test:

?0: ? = 0.40

? A  : ? ≠ 0.40

?'= 1-0.4=0.6

LEVEL OF SIGNIFICANCE =0.01

TEST STATISTIC

Z= p-?/sqrt(?*?'/n)

Z= 0.42-0.4/sqrt(0.4*0.6/64)

Z= 0.02/0.0612

Z= 0.3268

Z statistic =0.33

Critical Value of Z for two tailed test is 2.58 at alpha=0.01

Rejection Rule: R={If Z cal>2.58 then Reject H0}

Since Z cal SMALLER than Z critical .

Decision: DO NOT REJECT H0.

Conclusion: We don't have sufficient evidence to conclude that the proportion is different from 0.4