CONFIDENCE INTERVAL BUS708 TUTORIAL 7 Objectives: O1 Interval estimate based on margin of error 02 Confidence interval for the proportion 03 Confidence interval for the mean Tutorial Questions Q1). A survey of 1,000 American adults conducted in January 2013 stated that "44% say it's too hard to adopt a child in the US." The survey goes on to say that "The margin of sampling error is +/- 3 percentage points with a 95% level of confidence." a) What is the relevant sample statistic? Give appropriate notation and the value of the statistic. b) What population parameter are we estimating with this sample statistic? c) Use the margin of error to give a confidence interval for the estimate. Cholamiles gist d) Is 0.42 a plausible value of the population proportion? Is 0.50 a plausible value? Q2). In a random sample of 1500 US adults, 780 of them are "Thriving" which is defined as rating their current life as 7 or higher on a 10-point scale and rating their future life as 8 or higher on a 10-point scale. a). Find and interpret a 99% confidence interval for the proportion of all US adults who are thriving (based on this definition.) b). Do you believe that the proportion of all US adults who are thriving (based on this definition) could be 55%? Q3). Eleven people were given 46 grams (1.6 ounces) of dark chocolate every day for two weeks, and their vascular health was measured before and after the two weeks. Larger numbers indicate greater vascular health, and the mean increase for the participants was 1.3 with a standard deviation of 2.32. Assume a dot plot shows the data are reasonably symmetric with no extreme values. a) Find and interpret a 90% confidence interval for the mean increase in this measure of vascular health after two weeks of eating dark chocolate. b) Can we be 90% confident that the mean change for everyone would be positive? c) What is the margin of error for the confidence interval