I knew the formula for SE but fumbled a bit explaining why we use the sample proportion in it rather than the null value.
First, clearly state the null and alternative hypotheses for a one-sided test. Then, compute the standard error using the sample proportion, find the margin of error for 95% confidence, construct the confidence interval, and compare it to the null value to make a decision. Finally, interpret the result in the context of the billboard campaign.
Pro tip: When interpreting the confidence interval, emphasize that it provides a range of plausible values for the true conversion rate; if the null value falls outside this range, we reject the null. Also, mention that the one-sided test is appropriate if we only care about whether the conversion rate is greater than 60%.
Define the null hypothesis (H0: p = 0.60) and the alternative hypothesis (H1: p > 0.60) for a one-sided test.
Calculate the standard error using the sample proportion (0.65) and sample size (100): SE = sqrt(p_hat * (1 - p_hat) / n).
For a 95% confidence level, the critical z-value is 1.645 for a one-sided test. Margin of error = 1.645 * SE. The confidence interval is p_hat ± margin of error.
Check if the null value (0.60) falls outside the confidence interval. If it does, reject H0 at the 0.05 significance level. Explain that this means there is sufficient evidence to conclude the true conversion rate is greater than 60%.
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