For the following questions, a record label was curious to see if each member of one of their groups was equally preferred by fans of the group. There are 7 members in this group and 630 people responded to the poll posted on the record label’s website asking everyone to pick their favorite member of the group. The results were as follows. Member Initials RM SJ SG JH JM V JK
# Preferred 82 87 89 75 67 33 57

a. What would be the correct null and alternative hypotheses if you wanted to see if there was evidence of a difference in preference for the members of the group?
b. How many degrees of freedom would there be for a hypothesis test comparing how these preferences are split assuming each member of the group is equally preferred?
c. What would be the correct expected value for each member of the group, assuming each group member was equally preferred?
d. What would be the correct test statistic for a goodness-of-fit test, assuming each member of the group is equally preferred? Round your answer to one decimal place.
e. What would be the correct critical value for this test, for an alpha=0.05? Round to three decimal places.
f. What would be the correct p-value for this test? Round to one decimal place.
g. What would be the correct conclusion in context?

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

the results from a pre-test for students for the year 2000 and the year 2010 are illustrated in the box plot. what do these results tell us about how students performed on the 29 question pre-test for the two years?

if we compare only the lowest and highest scores between the two years, we might conclude that the students in 2010 did better than the students in 2010. this conclusion seems to follow since the lowest score of 8 in 2010 is greater in value than the lowest score of 6 in 2000. also, the highest score of 28 in 2010 is greater in value than the highest score of 27 in 2000.

but the box portion of the illustration gives us more detailed information. the middle bar in each box shows us that the median score of 20 in 2000 is greater in value than the median score of 17 in 2010. further, we note that the box and whiskers divide the illustration into four pieces. each of these four pieces represents the same portion of students. so, the upper half of the students in 2000 scored in the same score range as the upper one-fourth of the students in 2010, see the illustration at a score of 20.

by considering the upper one-fourth, upper half, and upper three-fourths instead of just the lowest and highest scores, we would conclude that the students as a whole did much better in 2000 than in 2010. we would conclude that as a whole the students in 2010 are less prepared than the students in 2000.

in this section, we discuss box-and-whisker plots and the five key values used in constructing a box-and-whisker plot. the key values are called a five-number summary, which consists of the minimum, first quartile, median, third quartile, and maximum.

step-by-step explanation: