A student who is writing an article about music for the school newspaper asks an
ID: 3222506 • Letter: A
Question
A student who is writing an article about music for the school newspaper asks another student. Chin Sun, to estimate the mean length of the mp3 downloads available on a particular web site. Being an AP Statistic student, Chin Sun decides to make this estimate using a confidence 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, should Chin-Sun use 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
SolutionA;
she should use t distribution.
here sample size n=15
n<30
small sample and population standard deviation is not known,
hence use t distribution for critical value.When shall we go for Z distr is
when n>30 and population standard deviation is given.
Solution B:
95% confidence interval means we are 95% confident that the true population mean lies in this interval range.
Solutionc:
degrees of freedom=n-1=15-1=14
alpha=0.05
alpha/2=0.05/2=0.025
tcritical for 14 df and 0.025 level of significanc is 2.145
From confidence intervl given
margin of error=19.209
margin of error means tcritical *sample sd/sqrt(sample size)
2.145*sample sd/sqrt(15)=19.209
sample sd=19.209(sqrt(15))/2.145
=34.684
chin suns sample standard deviation is 34.684
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