Question

In: Statistics and Probability

iTunes library of mp3s has a very large number of songs. A student creates a playlist...

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.

Solutions

Expert Solution

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


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