4 Researchers are concerned about the impact of students wor

(4) Researchers are concerned about the impact of students working while they are enrolled in classes, and they\'d like to know if students work too much and therefore are spending less time on their classes than they should be. First, the researchers need to find out, on average, how many hours a week students are working. A random sample of 200 students resulted in a sample mean of 7.10 hours worked per week. They know from previous studies that the population standard deviation of this variable is about 5 hours.

Solution

a)
Confidence Interval
CI = x ± Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=7.1
Standard deviation( sd )=5
Sample Size(n)=200
Confidence Interval = [ 7.1 ± Z a/2 ( 5/ Sqrt ( 200) ) ]
= [ 7.1 - 1.96 * (0.35) , 7.1 + 1.96 * (0.35) ]
= [ 6.41,7.79 ]