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?