In a study of the accuracy of fast food drive-through orders, McDonald’s had 33 orders that were not accurate among 362 orders. Burger King had 40 orders that were not accurate among 400 orders. Construct a 95% confidence interval around the difference in the proportions of inaccurate orders for the two restaurants. Recall the formula for margin or error

A high school counselor is interested in determining factors that contribute to high school drop out rates. One factor of interest to her is whether kids who are involved in team sports as children are less likely to drop out of high school. She surveys 41 high school graduates and finds that 30 were involved in team sports as children. She then surveys 38 high school dropouts and finds that 23 were involved in team sports as children. Construct and interpret a 90% confidence interval for the true difference between the proportions of high school graduates and dropouts who participated in team sports as children.  Does this data suggest that there is a difference between these proportions at this level of confidence?  Correctly round your results to the nearest tenth of a percent (one decimal place) in the intepretation of your interval.

A researcher wanted to compare the percentages of men and women who play the lottery.  They randomly sampled 300 women and found that 66 of them play the lottery.  In a random sample of 500 men, they found that 160 of them play the lottery.  Construct a 90% confidence interval for the difference in the percentage of women and men who play the lottery. Find the point estimate. Find the margin of error. Interpret the confidence interval in terms of this problem.

An ice cream shop wants to know how many customers enjoy their newest flavor. 200 randomly selected customers who have tried the flavor were asked whether they liked it or not. 145 our of 200 answered that they liked it.    Using this data, construct a 99% confidence interval for the true proportion of customers who enjoyed the ice cream flavor.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 99% confidence interval to estimate the true proportion of students on financial aid.

Twenty years ago, a very famous psychologist specializing in marriage counseling authored a book detailing the way in which she believed spouses should communicate. She is now interested in the proportion of all couples who bought her book who stayed together. For a random sample of 275 couples who bought her book, she found that 217 of them stayed together. Based on this, compute a 90% confidence interval for the proportion of all couples who bought her book who stayed together. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the  90%  confidence interval?   What is the upper limit of the  90%  confidence interval?

An internet service provider sampled 540 customers and found that 55 of them experienced an interruption in their service during the previous month. Construct a 95% confidence interval for the proportion of all the customers who have experienced a service interruption. Interpret the results.

A therapist would like to evaluate an intervention for treating depression.  A sample of n = 20 depressed clients is obtained, and each person’s level of depression is measured using a standardized questionnaire before they begin the therapy program.  Two weeks after therapy, each client’s level of depression is measured again.  The average level of depression dropped by 4.0 points following therapy.  The difference scores had a variance of 64.  Identify and Cclculate the appropriate test statistic.Make sure to report the degrees of freedom for the statistical test (if appropriate).  You must show your work to receive full credit. State your conclusions (use a two-tailed test with a = .05 for all tests). Compute an effect size.

In a random sample of 600 adults, 270 described themselves as vegetarians. Construct a 99% confidence interval for the proportion of all adults who describe themselves as vegetarians.

In a survey of 2013 adults in a recent​ year, 731 made a New​ Year's resolution to eat healthier.   Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.