A 95 confidence interval for the mean hours freshmen spent o

A 95% confidence interval for the mean hours freshmen spent on social media per day was calculated to be (2.5 hrs, 3.1 hrs). The confidence interval was based on an SRS of size n=50. The standard deviation is given by

a. 0.2772

b. 0.3000

c. 1.9600

d. 1.0823

Solution

ME = (Upper Interval - Lower Interval) / 2 = (3.1 - 2.5) / 2 = 0.3
Margin of Error = Z a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
0.3 = Z a/2 ( s.d/ Sqrt ( n ) )
0.3 = 1.96 ( s.d/ Sqrt(50) )
s.d = 0.3*Sqrt(50)/1.96 = 1.0823