Suppose a random sample of 100 observations has produced 79

Suppose a random sample of 100 observations has produced 79 successes, and we wish to test the claim p < 0.86. Write the hypotheses of the test, calculate the value of the standardized z-statistic, find the significance (P-value) for the test, and complete the test using alpha = 0.05.

Solution

Answer: Ho: p = 0.86
Ha: p < 0.86 (claim)

z = (0.79 - 0.86)/sqrt(0.86*(1-0.86)/100)
= -2.0174

critical z = -1.65 at 0.05 level.

Hence, computed z (-2.0174) < critical z (-1.65).
So, reject Ho.

conclusion: There is enough evidence to support the claim