Final answer:
In hypothesis testing, when the p-value (0.0175) is less than the significance level (0.05), we reject the null hypothesis. For this question, since the p-value of 0.0175 is less than the alpha of 0.05, we would reject the null hypothesis that the population proportion p equals 0.2.
Step-by-step explanation:
The question involves hypothesis testing in statistics, which is a method used to determine if there is enough evidence to reject a given hypothesis about a population parameter. Specifically, the question is about testing a null hypothesis H0: p = .2 against an alternative hypothesis HA: p ≠ .2, using a sample proportion (π) of .26 and a sample size (n) of 100. The significance level (α) is .05.
Step by step, first, we calculate the test statistic using the provided sample proportion and sample size. Then, we compare the calculated p-value with the given significance level α. If the p-value is less than α, we reject the null hypothesis; if it's more, we fail to reject it. Given that the p-value is 0.0175, which is less than the alpha of 0.05, we would reject the null hypothesis (H0), concluding that there is sufficient evidence to suggest that the true population proportion p is not 0.2.