Researchers published a study that Investigated the degree to which a country's households waste food. The researchers used data from 3711 households to measure the percentage of food acquired that is wasted per household For this sample of 3,711 households the mean amount of food wasted is 32.5% with a standard deviation of 17.4% Complete parts a and b. a. Find a 95% confidence interval for mu the true mean amount of food wasted by all households. (square % .square % ) (Round to one decimal place as needed.) b. An economist claims that mu is less than 31% Do you agree? Explain. A. Yes, because 31% is outside the confidence interval. B. Yes, because 31% is inside the confidence interval C. No, because 31% is outside the confidence interval. D. No, because 31% is inside the confidence interval

a. To find the 95% confidence interval for the true mean amount of food wasted by all households, we can use the formula:<br /><br />Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √n)<br /><br />Where:<br />- Sample Mean = 32.5%<br />- Standard Deviation = 17.4%<br />- n = 3,711 (sample size)<br /><br />The critical value for a 95% confidence interval is approximately 1.96.<br /><br />Plugging in the values, we get:<br /><br />Confidence Interval = 32.5% ± (1.96) * (17.4% / √3,711)<br /><br />Calculating the margin of error:<br /><br />Margin of Error = 1.96 * (17.4% / √3,711) ≈ 2.1%<br /><br />Therefore, the 95% confidence interval for the true mean amount of food wasted by all households is:<br /><br />(32.5% - 2.1%, 32.5% + 2.1%) = (30.4%, 34.6%)<br /><br />b. To determine if the economist's claim that μ is less than 31% is correct, we need to compare the 31% value with the 95% confidence interval.<br /><br />The 31% value is within the 95% confidence interval of (30.4%, 34.6%).<br /><br />Therefore, the correct answer is:<br /><br />D. No, because 31% is inside the confidence interval.