For each of the following examples, state whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate, and state the degrees of freedom (df) for the test.

Part (a)

A student tests whether the professor's speaking style (monotone, dynamic) and student interest (low, average, high) are independent.

State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

chi-square goodness-of-fitchi-square test for independence

State the degrees of freedom for the test.

df =

Part (b)

An instructor tests whether class attendance (low, average, high) and grade point average (low, high) are independent.

State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

chi-square goodness-of-fitchi-square test for independence

State the degrees of freedom for the test.

df =

Part (c)

A health psychologist records the number of below average, average, and overweight individuals in a sample of college students.

State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

chi-square goodness-of-fitchi-square test for independence

State the degrees of freedom for the test.

df =

Part (d)

A sports psychologist compares the number of athletes with Type A or Type B personality traits.

State whether the chi-square goodness-of-fit test or the chi-square test for independence is appropriate.

chi-square goodness-of-fitchi-square test for independence

State the degrees of freedom for the test.

df =

Question 3 An electrical system consists of four components as illustrated below. The system works if components A and B work and either of the components C or D work. The reliability (probability of working) of each component is given as pA=0.94. pp=0.82. pc=0.96, pp=0.85. Assuming that four components work independently, find the probability that: (8 pts.) PC A DO D Part a) The entire system works. (2 pts.) Part b) # The component C does not work, given that the entire system works. (3 pts.) Part c) The entire system works given that the component C does not work. (3 pts.)rou Hand 1 Fa20 Fa20 Micro Mod Class G funct Biost Micro Sign H X cture.com/courses/1295643/quizzes/1439355?module_item_id=10338094 ct) - ger... B RStudio Question 20 1.2 / 1.2 pts The equilibrium constant K for the synthesis of ammonia is 6.8x10' at 298 K. What will K be for the reaction at 375 K? N2(g) + 3H2(g) = 2NH3(g) AH =-92.22 KJ/mol 6.75 x 105 1.42 x 109 O 6.85 x 105 O 3262 (20) 3. For the matrix A = 3 1 1 2 a.) Find all eigenvalues of the matrix. b.) Find all eigenvectors of the matrix. c.) Is the matrix diagonalizable? If so, state a matrix P and a diagonal matrix D for which P-1AP = D. Page 4