In: Statistics and Probability
iTunes library of mp3s has a very large number of songs. A student creates a playlist of 45 randomly selected songs. The sample mean length of the songs is 241.27 seconds and the standard deviation is 93.40 seconds.
Note: Numbers are randomized in each instance of this question. Pay attention to the numbers in this question.
What is the lower bound for a 95% confidence interval for the actual mean length of the songs? Give your answer to 4 decimal places.
Solution :
sample size = n = 45
Degrees of freedom = df = n - 1 = 44
t ,df = 2.015
Margin of error = E = t,df * (s /n)
= 2.015 * (93.40 / 45)
Margin of error = E = 28.0553
The 95% confidence interval estimate of the population mean is,
- E < < + E
241.27 - 28.0553 < < 241.27 + 28.0553
213.2147 < < 269.3253
Lower bound = 213.2147