obtained a interval for the of the 15.4 and of In 14.5 (page 356) , 15.5 of a to be Normally (a) Three 90% and of these three intervals is the 99% one is the inter you trust a repo typically address these issues in detail. APPLY YOUR KNOWLEDGE obtained a 95% confidence interval for the mean concentration of s) you ingredient in a pharmaceutical product. Here are three confidence inte active 0.84546), and (0.83398, 0.84689). (a) Three confidence levels were used: 80%, 90% and 99%. Which of these al intervals is the 99% confidence interval? Which one is the 80% confidence: e val? Explain your reasoning. (b) Which of these three intervals is the narrowest? Explain why the narrow interval in this set is not necessarily the most informative. 15.5 Sample size and margin of error. Consider a variable known to be Normall, distributed with unknown mean u and known standard deviation o = 10. (a) What would be the margin of error of a 95% confidence interval for the ponula tion mean µ based on a random sample of size 25? The multiplier for a z confidence interval with a 95% confidence level is the critical value z* = 1.960. (b) What would be the margin of error of a 95% confidence interval for u based on a random sample of size 100? Based on a random sample of size 400? (c) Compare the margins of error for samples of size 25, 100, and 400. How does increasing the sample size change the margin of error of a confidence interval? 15.6 Spending on food. A 2012 Gallup survey based on a random sample of 1014 American adults indicates that American families spend, on average, $15l per week on food. The report further states that, with 95% confidence, this esti- mate has a margin of error of ±$7. Explain whether the confidence interval cite accounts for the following sources of error.ta replaces t (a) The poll dialed telephone numbers at random and so missed all people witho phones. ma fev (b) Nonresponse-some people whose phone numbers were chosen never answe the phone in several calls or answered but refused to participate in the poll. GLIOT