Question

Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance alpha using the given sample statistics. Claim: pnot equals 0.27 ; alpha equals0.05 ; Sample statistics: ModifyingAbove p with caret equals0.23 , nequals 200

Answer 1

Here, we have: nP₀ = 200*0.27 = 54 > 10 and n(1 - P₀) = 200*0.73 = 146 > 10, therefore yes normal approximation could be used here.

The test statistic here is computed as:

Now if this is a one tailed test, the p-value here is computed as:

p = P(Z < -1.2742) = 0.1013 > 0.05 which is the level of signficance, therefore even for the two tailed test, p = 2*0.1013 = 0.2026 > 0.05

Therefore the test is not significant and we cannot reject the null hypothesis here that the proportion is equal to 0.27. Therefore we have insufficient evidence here to conclude that the proportion is different from 0.27