1. (5 pts) A marketing research company needs to estimate which of two medical plans itsemployees prefer. A random sample of n employees produced the following 95% confidenceinterval for the proportion of employees who prefer plan A. (0.299, 0.539) What is the pointestimate of the true proportion of employees who prefer that plan? What is the margin of error?2. (5 pts) A university dean is interested in determining the proportion of students who receivesome sort of financial aid. Rather than examine the records for all students, the dean randomlyselects 200 students and finds that 118 of them are receiving financial aid. Find a 99%confidence interval to estimate the true proportion of students on financial aid. Express theanswer in the form p-hat ± E and round to the nearest hundredth.3. (5 pts) A simple random sample of size n < 30 was taken. From the box plot, determinewhether we should find a t-intervalA. No, there are outliers and the data is not normally distributed but skewed right.B. No. Although there are no outliers, the data is not normally distributed but is skewedright.C. Yes, the data are normally distributed and there are no outliers.D. No, the data is normally distributed but there are outliers.4. (5 pts) From a population that has a normal distribution, a sample of 15 randomly selectedmath majors has a grade point average of 2.86 with a standard deviation of 0.78. Find the 90%confidence interval for the population mean ?. Round to the nearest hundredth.5. (5 pts) The principal of a school randomly selected six students to take an aptitude test. Theirscores were:? 78.2 81.3 86.1 84.2 72.8 85.2Assume that the population has anormal distribution. Find a 90 percent confidence interval for the mean score for all students.6. (5 pts) A researcher at a major clinic wishes to estimate the proportion of the adult populationof the United States that has sleep deprivation. How large a sample is needed in order to be99% confident that the sample proportion will not differ from the true proportion by more than5%?7. (5 pts) What is meant by the term â90% confident when constructing a confidence interval fora mean?8. (5 pts) The reading speed of second grade students is approximately normal with a mean of90 words per minute (wpm) and a standard deviation of 10 wpm. If you were to obtain 130different simple random samples of size 25 from the population of all second grade studentsand determine 90% confidence intervals for each of them, how many of the intervals would youexpect to include the reading speed of 90 wpm?9. (5 pts) Two researchers, Jaime and Maria, each construct confidence intervals for theproportion of a population who is left-handed. They find the point estimate is 0.13. Eachindependently constructs a confidence interval based on the point estimate. Jaimeâs interval is(0.097, 0.163) while Mariaâs interval is (0.117, 0.173). Which interval is wrong and why?10. (15 pts) The following small data set represents a simple random sample from a populationwhose mean is 50.436353505844535352415043A. A normal probability plot indicates that the data could come from a population that isnormally distributed with no outliers. Find a 95% confidence interval for this data set.B. Suppose the observation, 41, is mistakenly entered as 14. Show that this observation isan outlier.C. Find a 95% confidence interval with the data set containing the outlier. What effect doesthe outlier have on the confidence interval?11. (20 pts) From a random sample of 698 adult males 20 to 34 years of age, it was determinedthat 60 of them have hypertension (high blood pressure).A. Find a point estimate for the proportion of adult males 20 to 34 years of age who havehypertension.B. Construct a 95% confidence interval for the proportion of adult males 20 to 34 years of agewho have hypertension.C. You wish to conduct your own study to determine the proportion of adult males 20 to 34 yearsold who have hypertension. What sample size would be needed for the estimate to be within 3percentage points with a 95% confidence if you use the point estimate found in part a?D. You wish to conduct your own study to determine the proportion of adult males 20 to 34 yearsold who have hypertension. What sample size would be needed for the estimate to be within 3percentage points with a 95% confidence if you donât have a prior estimate?
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