## Related questions with answers

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 1.65 million households with a sample standard deviation of 0.56 million family units. Over the same 12 months WinMX was used by an average of 2.2 million families with a sample standard deviation of 0.30 million. Assume the population standard deviations are not the same. Using a significance level of 0.05, test the hypothesis of no difference in the mean number of households picking either variety of service to download songs.

Solution

VerifiedGiven:

$\begin{align*} n_1&=\text{Sample size}=12 \\ n_2&=\text{Sample size}=12 \\ \overline{x}_1&=\text{Sample mean}=1.65 \\ \overline{x}_2&=\text{Sample mean}=2.2 \\ s_1&=\text{Sample standard deviation}=0.56 \\ s_2&=\text{Sample standard deviation}=0.30 \\ \alpha&=\text{Significance level}=0.05 \end{align*}$

Given claim: No difference in the means

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis and the alternative hypothesis state the opposite of each other. The null hypothesis needs to include an equality.

$H_0:\mu_1=\mu_2$

$H_1: \mu_1 \neq \mu_2$

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