Stat200 Quiz 3 2016 oct

University of University College

Stat 200 (Whealon) Quiz 3 – 80 pts

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1. (5 pts) A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the following 95% confidence interval for the proportion of employees who prefer plan A. (0.299, 0.539) What is the point estimate 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 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. Find a 99% confidence interval to estimate the true proportion of students on financial aid. Express the answer 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, determine whether we should find a t-interval

a. 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 skewed right.

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 selected math 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. Their scores were:
78.2 81.3 86.1 84.2 72.8 85.2
Assume that the population has a normal 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 population of the United States that has sleep deprivation. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 5%?

7. (5 pts) What is meant by the term “90% confident when constructing a confidence interval for a mean?

8. (5 pts) The reading speed of second grade students is approximately normal with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm. If you were to obtain 130 different simple random samples of size 25 from the population of all second grade students and determine 90% confidence intervals for each of them, how many of the intervals would you expect to include the reading speed of 90 wpm?

9. (5 pts) Two researchers, Jaime and Maria, each construct confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently constructs a confidence interval based on the point estimate. Jaime’s interval is (0.097, 0.163) while Maria’s 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 population whose mean is 50.

43	63	53	50	58	44
53	53	52	41	50	43

a. A normal probability plot indicates that the data could come from a population that is normally 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 is an outlier.

c. Find a 95% confidence interval with the data set containing the outlier. What effect does the 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 determined that 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 have hypertension.

b. Construct a 95% confidence interval for the proportion of adult males 20 to 34 years of age who have hypertension.

c. You wish to conduct your own study to determine the proportion of adult males 20 to 34 years old who have hypertension. What sample size would be needed for the estimate to be within 3 percentage 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 years old who have hypertension. What sample size would be needed for the estimate to be within 3 percentage points with a 95% confidence if you don’t have a prior estimate?