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The Township Board of Meridian Township wants to know how much public support there is for rezoning an area of the township for higher-density housing. In their quarterly Township newsletter, town officials report that $36%$ of a random sample of Township residents are in favor of the rezoning proposal. In the fine print at the bottom of the article, the report states that the estimated standard error for the proportion based on their sample is $SE_{p?}=0.06$. The report does not give the size of the sample used. 1. What is the correct interpretation of this standard error? A. We expect any repeated sample proportion of the same number of residents used for this report to be wrong approximately $6%$ of the time, on average. B. We can be $6%$ confident that our sample proportion will be contained in any confidence interval we construct using this value. C. We have strong evidence that, on average, a new sample will give a sample proportion within 0.06 of the lower and upper bounds of the confidence interval we construct with this value. D. In repeated samples of the same number of residents used for this report, we will expect, on average, the sample proportions to be within 0.06 of the actual proportion of residents in favor of the rezoning. 2. Use the information given to calculate a $95%$ confidence interval for the actual proportion of Meridian Township residents who are in favor of the rezoning proposal. Hint: You will need to use a formula for this calculation. 3. What is the margin of error for the $95%$ confidence interval you ca?curateoningaitzz?
D. In repeated samples of the same number of residents used for this report, we will expect, on average, the sample proportions to be within 0.06 of the actual proportion of residents in favor of the rezoning. 2. Use the information given to calculate a $95%$ confidence interval for the actual proportion of Meridian Township residents who are in favor of the rezoning proposal. Hint: You will need to use a formula for this calculation. 3. What is the margin of error for the $95%$ confidence interval you calculated in part 2 ? Margin of error $=$ 4. A local political action group decides to repeat the survey of Meridian Township residents and obtains the same sample proportion, $p^?$, as the Township Board. Consider the statement: If the sample size used by the political action group is smaller than the sample used for the Township newsletter, then their estimated standard error will be less than 0.06 . Is this statement always true or sometimes true or never true? A. Always true B. Sometimes true C. Never true

Given that =SE = 0.06p = 0.36And CI = 95

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