A survey was conducted (last year) on whether or not STAT 225 students listened

Question

A survey was conducted (last year) on whether or not STAT 225 students listened to Spotify while they were studying for the final exam. Each student was classified by instructor and by whether they listened to Spotify or did not listen. Some of the data is shown in the table below. a) Fill in the missing entries in the table using the information provided. b) A student is chosen at random, what is the probability that the student is from Jessi's class. Is this a marginal, joint or conditional probability? c) Given that a randomly chosen student does listen to Spotify while studying, what is the probability the student is in Will's class? Is this a marginal, joint or conditional probability? d) Write out the hypotheses for the Chi-Square(X^2) test of this data. e) Create a table of expected counts. f) Finish the table of partial X^2 values. g) What is the value of the X^2 statistic? What are its degrees of freedom? h) Using alpha = 0.05, state the conclusion of the Chi-Square (X^2) test in the context of this problem. State your reasoning behind your conclusion.

Explanation / Answer

(A) Missing entries or say COmpletely filled observed table

(B) A student is chosen randomly out of 175 students and number of students in jessi's class = (56)

so Pr( Jessi) = 56/175 = 0.32

It is the case of marginal probability .

(C) A chosen student does listen to spotify while studying . So total number of such students are 98 and out of which Will' class have 17 such students.so

Pr( Will when students does listen to spotify) = 17/98 = 0.1735

(D) Null Hypothesis : There is no difference in proportion of students listen to spotify for different -2 instructors.

Alternative Hypothesis : There is significant difference in proportion of students listen to spotify for different-2 instructors.

(e) Expected Table

(f) partial X2table

(g) X2= sum of all partial values = 6.2314

Degree of freedom = (4-1) * (2-1) = 3

(h) for alpha = 0.05 X2critical = 7.815

so here X2< X2critical , so we cannot reject the null hypothesis and conclude that there is no significant difference between proportion of listener students across various instructors.

Will Jessi Tim Megan Total Listened to spotify 17 34 27 20 98 Did not listen to spotify 25 22 14 16 77 total 42 56 41 36 175

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