A study was carried out to understand the amount of time put in by the students in three management institutes. One hundred students from different institutions were surveyed. Information regarding the hours put in by the students per week is summarized in the following contingency table:
Institution <= 40 hours/week between 40 and
<= 45 hours/week More than 45 and
<=50 hours/week more than
50 hours/week
A 2 8 20 20
B 4 6 10 10
C 3 4 7 6
a) What is the proportion of students who put in more than 45 hours a week? Calculate a 95 percent confidence interval for the population proportion of students who work more than 45 hours a week.
b) Is there any statistically significant evidence of any dependence between the number of hours put in by the students and the institution they belong to?