One of the music industry\'s most pressing questions is: Can paid download store
ID: 3319992 • Letter: O
Question
One of the music industry's most pressing questions is: Can paid download stores contend nose-to-nose with free peer-to-peer download services? Data gathered over the last 12 months show Apple's iTunes was used by an average of 1.70 million households with a sample standard deviation of .49 million family units. Over the same 12 months WinMX (a no-cost P2P download service) was used by an average of 2.12 million families with a sample standard deviation of .32 million. Assume the population standard deviations are not the same.
Find the degrees of freedom for unequal variance test. (Round down your answer to nearest whole number.)
Compute the value of the test statistic. (Negative amount should be indicated by a minus sign.Round your answer to 2 decimal places.)
Test the hypothesis of no difference in the mean number of households picking either variety of service to download songs. Use the .01 significance level.
(select) Do not reject or reject H0. There is (select) a significant or no significant difference in the mean number of households picking either variety of service to download songs.
One of the music industry's most pressing questions is: Can paid download stores contend nose-to-nose with free peer-to-peer download services? Data gathered over the last 12 months show Apple's iTunes was used by an average of 1.70 million households with a sample standard deviation of .49 million family units. Over the same 12 months WinMX (a no-cost P2P download service) was used by an average of 2.12 million families with a sample standard deviation of .32 million. Assume the population standard deviations are not the same.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 0.169
DF = 22
t = [ (x1 - x2) - d ] / SE
t = - 2.49
tcritical = 2.82
Rejection region is - 2.82 > t > 2.82
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 22 degrees of freedom is more extreme than - 2.49; that is, less than - 2.49 or greater than 2.49.
Thus, the P-value = 0.021.
Interpret results. Since the P-value (0.021) is greater than the significance level (0.01), we have to accept the null hypothesis.
Do not reject H0. There is no significant difference in the mean number of households picking either variety of service to download songs.
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