Question

In: Statistics and Probability

Professor Stone complains that student teacher ratings depend on the grade the student receives. In other...

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.

RatingABCF (or withdrawal)Row Total

Excellent151715552

Average25307012137

Poor23264319111

Column Total637312836300

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


State the null and alternate hypotheses.

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: Student grade and teacher rating are independent.
H1: Student grade and teacher rating 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 ≥ α, we reject the null hypothesis.Since the P-value ≥ α, we do not reject the null hypothesis.    Since the P-value < α, we do not reject the null hypothesis.Since the P-value < α, we 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.    

Solutions

Expert Solution

using excel>addin<phstat>multiple sample test

we have

Chi-Square Test
Observed Frequencies
Column variable Calculations
Row variable A B C F Total fo-fe
Excellent 15 17 15 5 52 4.08 4.346667 -7.18667 -1.24
Avergae 25 30 70 12 137 -3.77 -3.33667 11.54667 -4.44
Poor 23 26 43 19 111 -0.31 -1.01 -4.36 5.68
Total 63 73 128 36 300
Expected Frequencies
Column variable
Row variable A B C F Total (fo-fe)^2/fe
Excellent 10.92 12.65333 22.18667 6.24 52 1.524396 1.493165 2.327893 0.24641
Avergae 28.77 33.33667 58.45333 16.44 137 0.494018 0.333967 2.280888 1.199124
Poor 23.31 27.01 47.36 13.32 111 0.004123 0.037767 0.401385 2.422102
Total 63 73 128 36 300
Data
Level of Significance 0.01
Number of Rows 3
Number of Columns 4
Degrees of Freedom 6
Results
Critical Value 16.81189
Chi-Square Test Statistic 12.76524
p-Value 0.046919
Do not reject the null hypothesis

(i) the value of the level of significance is 0.01

the null and alternate hypotheses.

H0: Student grade and teacher rating are independent.
H1: Student grade and teacher rating are not independent.


(ii) the sample test statistic=12.77


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

0.025 < P-value < 0.050


(iv) Conclude the test.

Since the 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


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