Question

QUESTION 34 Problem 5) Final scores of all the students in randomly selected 3 sections in a course, "Statistical Methods at Sam Houston State University we presented below. There are 25 secil Section 3 (69.92, 66, 81, 76, 55, 70, 83, 68, 57, 50, 66, 69, 55, 88, 70, 70, 70,56,50) Section 6 (10, 73, 88, 58, 59, 69,63, 76, 87, 82, 97, 76, 66,95, 84, 88, 82, 81, 65, 89) Section 9. (30,85, 76, 73, 92, 65, 90, 71, 77, 78, 86, 91, 87, 78, 88, 77, 73,97, 86, (13) Let us assume that the passing score of this course is 70., a student with 70 or more in his her final score would pass the cow) Now, or of the core beste proports of the number of passing students in section 9 is different from section 6 Perform a proper hypothesis test and give the p-value of the test

Answer 1

The passing marks is 70 i.e a student scoring 70 or more will pass.

In section 6, 14 students have passed i.e propotion p1 =14/20=0.7

In section 9, 18 students have passed i.e propotion p2 =18/20=0.9

Overall propotion of students who passed is p = (14+18)/40 = 0.8

Our hypothesis is defined as :

Null hypothesis H0: p1=p2

Alternate hypothesis H1 : p1 $\neq$ p2

let level of significance be 5 %

The test statistic is given by :

(1-f2) - 0 Z= 1 Þ(1-P) (m + ni n2

$z =\frac{ (0.7 - 0.9)}{\sqrt{0.8(1-0.8)(\frac{1}{20}+\frac{1}{20})}}$

$z =\frac{ -0.2}{\sqrt{0.8(0.2)(\frac{1}{10})}}$

$z =\frac{ -0.2}{0.1265} =1.5810$

The value of z is -1.5811. The value of p is .1141. The result is not significant at p < .05.

We accept null hypothesis that is the proportion of students in section 6 and 9 are same.