Professor Stone complains that student teacher ratings depend on the grade the student receives. In other words, according to Professor Stone, a teacher who gives good grades gets good ratings, and a teacher who gives bad grades gets bad ratings. To test this claim, the Student Assembly took a random sample of 300 teacher ratings on which the student's grade for the course also was indicated. The results are given in the following table. Test the hypothesis that teacher ratings and student grades are independent at the 0.01 level of significance.

Rating A B C F (or withdrawal) Row Total

Excellent 14 18 16 2 50

Average 25 35 75 15 150

Poor 21 27 40 12 100

Column Total 60 80 131 29 300

Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square goodness of fit, Chi-square for testing ?² or ?.

Chi-square goodness of fitChi-square for testing ?² or ?    Chi-square test of independenceChi-square test of homogeneity

(i) Give the value of the level of significance.

State the null and alternate hypotheses.

H₀: Student grade and teacher rating are independent.
H₁: Student grade and teacher rating are not independent.H₀: The distributions for the different ratings are the same.
H₁: The distributions for the different ratings are different.    H₀: Ratings of excellent, average, and poor are independent.
H₁: Ratings of excellent, average, and poor are not independent.H₀: Tests A, B, C, F (or withdrawal) are independent.
H₁: Tests A, B, C, F (or withdrawal) are not independent.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(iv) Conclude the test.

Since the P-value < ?, we reject the null hypothesis.Since the P-value ≥ ?, we fail to reject the null hypothesis.    Since the P-value ≥ ?, we reject the null hypothesis.Since the P-value < ?, we fail to reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that student grade and teacher rating are not independent.At the 1% level of significance, there is sufficient evidence to claim that student grade and teacher rating are not independent

Question

Professor Stone complains that student teacher ratings depend on the grade the student receives. In other words, according to Professor Stone, a teacher who gives good grades gets good ratings, and a teacher who gives bad grades gets bad ratings. To test this claim, the Student Assembly took a random sample of 300 teacher ratings on which the student's grade for the course also was indicated. The results are given in the following table. Test the hypothesis that teacher ratings and student grades are independent at the 0.01 level of significance.

Rating	A	B	C	F (or withdrawal)	Row Total
Excellent	14	18	16	2	50
Average	25	35	75	15	150
Poor	21	27	40	12	100
Column Total	60	80	131	29	300

Classify the problem as one of the following: Chi-square test of independence or homogeneity, Chi-square goodness of fit, Chi-square for testing ?² or ?.

Chi-square goodness of fitChi-square for testing ?² or ? Chi-square test of independenceChi-square test of homogeneity

(i) Give the value of the level of significance.

State the null and alternate hypotheses.

H₀: Student grade and teacher rating are independent.
H₁: Student grade and teacher rating are not independent.H₀: The distributions for the different ratings are the same.
H₁: The distributions for the different ratings are different. H₀: Ratings of excellent, average, and poor are independent.
H₁: Ratings of excellent, average, and poor are not independent.H₀: Tests A, B, C, F (or withdrawal) are independent.
H₁: Tests A, B, C, F (or withdrawal) are not independent.

(ii) Find the sample test statistic. (Round your answer to two decimal places.)

(iii) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100 0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(iv) Conclude the test.

Since the P-value < ?, we reject the null hypothesis.Since the P-value ≥ ?, we fail to reject the null hypothesis. Since the P-value ≥ ?, we reject the null hypothesis.Since the P-value < ?, we fail to reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to claim that student grade and teacher rating are not independent.At the 1% level of significance, there is sufficient evidence to claim that student grade and teacher rating are not independent

Accepted Answer

Given:
Observed frequency table:

Rating
A
B
C
F (or withdrawal)
Row Total

Excellent
14
18
16
2…