Question

You wish to test the following claim a significance level of α = 0.01 . H o : p = 0.58 H a : p ≠ 0.58 You obtain a sample of size n = 186 in which there are 102 successful observations. What is the test statistic for this sample? test statistic = Round to 3 decimal places. What is the p-value for this sample? P-value = Use Technology Round to 4 decimal places.

Answer 1

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First we need to check the conditions of normality.

That is if np and n*(1-p) both are greater than 5 or not

N = 186 and P = 102/186

N*P = 102

N*(1-P) = 84

As both are greater than 5

We can use standard normal distribution z for the test

Test statistics z = (observed p - claimed p)/standard error

Standard error = √claimed p*(1-claimed p)/√n

N = sample size = 186

Claimed p = 0.58

Observed p = 102/186

Z = −0.873538824474

= -0.874

From z table p(z<-0.87) = 0.1922

But this is for one tail

For two tails, P-value = 2*0.1922

(Note this is two tailed test)

P-value = 0.3844