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In: Statistics and Probability

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

15) 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 240.52 seconds and the standard deviation is 94.47 seconds.

What is the upper bound for a 95% confidence interval for the actual mean length of the songs? Give your answer to 4 decimal places.

Your Answer:

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Expert Solution

Solution :


Given that,

Point estimate = sample mean =     = 240.52

Population standard deviation =    = 94.47

Sample size n =45

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

Z = Z0.05 = 1.645 ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.645 * ( 94.47 / 45 )

= 23.1661
At 95% upper confidence interval population mean
is,

< + E

< 240.52 + 23.1661

< 263.6861

Answer:263.6861

orchestra answered 3 years ago
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