Homework Assignments

Textbook #1: Lane et al. Introduction to Statistics, David M. Lane et al., 2013.

(http://onlinestatbook.com/Online_Statistics_Education.pdf)

Textbook #2:Illowsky et al. Introductory Statistics, Barbara Illowsky et al., 2013.

(http://openstaxcollege.org/files/textbook_version/hi_res_pdf/15/col11562-op.pdf)

See the file named "UMUC_STAT200_EXCEL_Tips" at the "Course Materials" menu link to find functions for calculating the Normal Distribution andStudent's T-distribution values needed for this assignment.

Lane - Chapter 10: 4,12,15,18

1. Why is a 99% confidence interval wider than a 95% confidence interval?

2. A person claims to be able to predict the outcome of flipping a coin. Thisperson is correct 16/25 times. Compute the 95% confidence interval on theproportion of times this person can predict coin flips correctly. What conclusion can you draw about this test of his ability to predict the future?

3. You take a sample of 22 from a population of test scores, and the mean of yoursample is 60. (a) You know the standard deviation of the population is 10.What is the 99% confidence interval on the population mean. HINT: Use the Z-score from the Normal Distribution(b) Now assumethat you do not know the population standard deviation, but the standarddeviation in your sample is 10. What is the 99% confidence interval on themean now?HINT: Use the Student's T-table

4. You were interested in how long the average psychology major at your collegestudies per night, so you asked 10 psychology majors to tell you the amountthey study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.(a) Find the 95% confidence interval on the population mean. (b) Find the 90%confidence interval on the population mean.HINT: Be sure to use the Student's T-table for each solution since you have a limited set of samples.

Illowsky - Chapter 8 (100,106,112,116,120,130)

100. What is meant by the term "90% confident" when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.
b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldcontain the sample mean.
c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples wouldcontain the true value of the population mean.
d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of thesamples.

106. Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested inthe mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomlysurveyed 81 people who recently served as jurors. The sample mean wait time was 8 hours with a sample standarddeviation of 4 hours.

a. Find: X ¯, Sx, N, N-1
b. Define the random variablesX ¯ in words.
c. Which distribution should you use for this problem? Explain your choice.
d. Find the 95% confidence interval for the population mean time wasted.
e. Explain in a complete sentence what the confidence interval means.

112. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a sample standard deviation of $3,156.

a. Which distribution should you use for this problem? Explain your choice.
b. Define the random variable X ¯ in words.
c. Find the 95% confidence interval
d. Explain what a "95% confidence interval" means for this study.

116. A quality control specialist for a restaurant chain takes arandom sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.30 with asample standard deviation of 1.55. What is the error bound of the 95% confidence interval?HINT: Be sure to use the Student's T-table for your solution since you are using a random sample and you do not know information about the population standard deviation.

120. An article regarding interracial dating and marriage recently appeared in the Washington Post. Of the 1,709 randomlyselected adults, 315 identified themselves as Latinos, 323 identified themselves as blacks, 254 identified themselves asAsians, and 779 identified themselves as whites. In this survey, 86% of blacks said that they would welcome a white personinto their families. Among Asians, 77% would welcome a white person into their families, 71% would welcome a Latino,and 66% would welcome a black person.HINT: See Section 8.3 (A Population Proportion)

a. We are interested in finding the 95% confidence interval for the percent of all black adults who would welcome awhite person into their families. Define the random variables X and P′, in words.
b. Which distribution should you use for this problem? Explain your choice.
c. Find the 95% confidence interval and error bound.

130. On May 23, 2013, Gallup reported that of the 1,005 people surveyed, 76% of U.S. workers believe that they willcontinue working past retirement age. The confidence level for this study was reported at 95% with a +/- 3% margin of error.

a. Determine the estimated proportion from the sample.
b. Determine the sample size.
c. Identify CL and α.
d. Calculate the error bound based on the information provided.
e. Compare the error bound in part d to the margin of error reported by Gallup. Are they the same?
f. Create a confidence interval for the results of this study.