A student who is writing an article about music for the school newspaper asks an
ID: 3222557 • Letter: A
Question
A student who is writing an article about music for the school newspaper asks another student, Chin-Sum, to estimate the mean length of the mp3 downloads available on a particular web site. Being an AP Statistics student, Chin-Sun decides to make this estimate using a confidence interval. She randomly selects 15 songs from the site, and makes note of their lengths in seconds. Chin-Sun then uses these results to construct a 95% confidence interval for the mean length of all songs on the site. Prior to gathering this sample, Chin-Sun has no knowledge of the lengths of the songs on the site. (A) In order to find the critical value to use in the calculation of her confidence interval, souls Chin-Sun use the standard normal (z) distribution or a t distribution? Explain your answer. (b) What is the meaning of 95% confidence in this context? (c) Using the results from her sample, Chin-Sun checks and verifies all the conditions for inference, and correctly calculates the confidence interval for the mean length (in seconds) of all songs on the site to be 242.733 plusminus 19.209. What was the standard deviation of the song lengths in Chin - Sun's sample?Explanation / Answer
a) she must use t-distribution as we do not know about population distribution as well sample size is small
b)95% confidence interval is the interval which gives 0.95 probability to contain true population mean of length of songs
c)here margin of error E =19.209
for (n-1=14) degree of freedom ; t=2.1448
hence std error =19.209/2.1448=8.956
therefore std deviation =std error*(n)1/2 =34.6870
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