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 12 19 12 5 48 Average 23 33 72 15 143 Poor 25 28 45 11 109 Column Total 60 80 129 31 300 (i) Give the value of the level of significance. State the null and alternate hypotheses. H0: Ratings of excellent, average, and poor are independent. H1: Ratings of excellent, average, and poor are not independent. H0: The distributions for the different ratings are the same. H1: The distributions for the different ratings are different. H0: Tests A, B, C, F (or withdrawal) are independent. H1: Tests A, B, C, F (or withdrawal) are not independent. H0: Student grade and teacher rating are independent. H1: Student grade and teacher rating 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. (Round your answer to three decimal places.) (iv) Conclude the test. Since P-value < α, we reject the null hypothesis. hypothesis. Since P-value ≥ α, we reject the null Since P-value ≥ α, we do not reject the null hypothesis. Since P-value < α, we do not 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.
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