Question

In: Statistics and Probability

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

iTunes songs ~ 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 240.14 seconds and the standard deviation is 92.34 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

Given that,

= 240.14

s = 92.34

n = 45

Degrees of freedom = df = n - 1 = 45 - 1 = 44

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

t,df = t0.05,44 = 1.680

Margin of error = E = t,df * (s /n)

= 1.680 * (92.34 / 45)

= 23.1256

The 95% confidence interval estimate of the population mean is,

- E < < + E

240.14 - 23.1256 < < 240.14 + 23.1256

217.0144 < < 237.2656

Lower bound = 217.0144

orchestra answered 2 years ago
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