A random sample of 60 teenagers revealed that teenagers rece

A random sample of 60 teenagers revealed that teenagers received an average 2,272 text messages per month. Assume the population standard deviation is 953 text messages per month. Construct a 99% confidence interval. Write your answer in the interval notation: \"(lowerbound, upperbound)\"

Solution

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)=2272
Standard deviation( sd )=953
Sample Size(n)=60
Confidence Interval = [ 2272 ± Z a/2 ( 953/ Sqrt ( 60) ) ]
= [ 2272 - 2.58 * (123.032) , 2272 + 2.58 * (123.032) ]
= [ 1954.578,2589.422 ]