CMP MAT 20020105 Ken Flowers A researcher wishes to estimate, with 95\% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Her estimate must be accurate within \( 4 \% \) of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that \( 20 \% \) of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? as needed.) (Round up to the nearest whole number and

\#2 A survey was taken comparing the number of hours per week students spent studying and their performance on an exam. If a linear regression was performed and the correlation coefficient was -0.017 , what can be said about these results? a. As the number of hours spent studying increases, student exam performances will likely not change. b. As the number of hours spent studying inrceases, student exam performances will probably increase. c. As the number of hours spent studying increases, student exam performances will probably decrease. d. There is little evidence of a linear relationship between the number of hours spent studying and student exam performances.

Find the mean for the following group of data items. \[ 7.4,5.7,9.2,6.8,2.2,2.5,9.5,6.5,7.2,5.6,1.2 \] The mean is \( \square \). (Round to 3 decimal places as needed.)

\#3 A set of data has correlation coefficient \( r \). For which value of \( r \) would the average magnitude of the residuals be the largest? a. \( r=-0.516 \) b. \( r=-0.445 \) c. \( r=0.875 \) d. \( r=0.158 \)

\#7 A set of data has correlation coefficient \( r \). For which value of \( r \) would the average magnitude of the residuals be the smallest? a. \( r=-0.034 \) b. \( r=0.472 \) c. \( r=0.908 \) d. \( r=0.952 \)

Suppose you are interested in whether or not the students at your high school would favor a grading system in which students may receive final grades of \( \mathrm{A}+, \mathrm{A}, \mathrm{A}-, \mathrm{B}+, \mathrm{B}, \mathrm{B}-, \mathrm{C}+, \mathrm{C}, \mathrm{C}- \), and so on. Describe how you might obtain a random sample of 100 students from the entire student population. Choose the correct answer below. A. Assign each student at the school a number, write each number on a card, and place all of the cards in a box. Then, randomly select 100 cards. B. Post an advertisement requesting the assistance of 100 students. Among the first 100 students to arrive, select them in a random order. C. Sort the students by their overall average grades. Then, select the 50 students with the best grades and the 50 students with the worst grades. D. Determine the ten streets on which the most students at the school live. Then, select ten students from each street. If fewer than ten students live on a street, fill in the spot with a randomly selected student.