Question

In: Statistics and Probability

The table lists the number of students from three different high schools participating in the mathematics...

The table lists the number of students from three different high schools participating in the mathematics and physics sections of a science fair High School 1 High School 2 High School 3 Mathematics 7 7 18 Physics 37 17 21

Given the following results.

a) State the alternative hypothesis statement. (1 mark)

b) State the degrees of freedom. (1 mark)

c) Find the value of A, B, and C. d) Using the p-value method, at α = 0.05, test the claim that the section of participation and the high school where the students were from are independent.

Solutions

Expert Solution

(a) The section of participation and the high school where the students were from are dependent

(b) 2

(c)

High School 1   High School 2   High School 3   Total  
Mathematics Observed   7 7 18 32
Expected   13.16 7.18 11.66 32.00
O - E   -6.16 -0.18 6.34 0.00
(O - E)² / E   2.88 0.00 3.44 6.33
Physics Observed   37 17 21 75
Expected   30.84 16.82 27.34 75.00
O - E   6.16 0.18 -6.34 0.00
(O - E)² / E   1.23 0.00 1.47 2.70
Total Observed   44 24 39 107
Expected   44.00 24.00 39.00 107.00
O - E   0.00 0.00 0.00 0.00
(O - E)² / E   4.11 0.01 4.91 9.03
9.03 chi-square
2 df
.0109 p-value

(d) The p-value is 0.0109.

Since the p-value (0.0109) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the section of participation and the high school where the students were from are dependent.

orchestra answered 2 years ago
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