A newspaper columnist writes that "a majority of Republicans believe that the 2020 election was stolen" What null hypothesis and alternative hypothesis should you use in testing that statement? \( \begin{array}{ll}\mathrm{H}_{0}: p>0.50 & \mathrm{H}_{\mathrm{a}}: p=0.50 \\ \mathrm{H}_{0}: p \neq 0.50 & \mathrm{H}_{\mathrm{a}}: p=0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p>0.50 \\ \mathrm{H}_{0}: p<0.50 & \mathrm{H}_{\mathrm{a}}: p=0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p \geq 0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p \neq 0.50 \\ \mathrm{H}_{0}: p=0.50 & \mathrm{H}_{\mathrm{a}}: p \leq 0.50 \\ \mathrm{H}_{0}: p \neq 0.50 & \mathrm{H}_{\mathrm{a}}: p>0.50\end{array} \)

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.

The accompanying data describes the earnings of 15 celebrities. Complete parts (a) through (d). a. Find the mean. The mean earnings of the 15 celebrities is \( \$ \square \) million. (Round to the nearest tenth as needed.)

\#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.)

Determine whether the following statement makes sense or does not make sense. Although the data set \( 5,5,6,6,6,7,7,7 \) has a number of repeated items, there is only one mode. Choose the correct answer below. A. The statement does not make sense because there are no modes in the data set. B. The statement makes sense because there is 1 mode in the data set. C. The statement does not make sense because every value is a mode in the data set. D. The statement does not make sense because there are 2 modes in the data set.