Related questions with answers

A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $57,000 with a standard deviation of$9,200. This distribution is positively skewed; the actual coefficient of skewness is 2.11. For a sample of 30 subscribers to Plan B, the mean income is $61,000 with a standard deviation of$7,100. The distribution of Plan B subscribers is also positively skewed, but not as severely. The coefficient of skewness is 1.54. At the .05 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? What is the p-value? Do the coefficients of skewness affect the results of the hypothesis test?Why?

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.

The proprietor of Bun 'N' Run Hamburgers wants to contrast the day sales at two different establishments. At the Northside site, the mean number sold over the course of ten days was 83.55, with a standard deviation of 10.50. The average number of sales for a random 12-day period at the Southside site was 78.80, with a standard deviation of 14.25. Is there a difference in the mean number of hamburgers sold at the two places at the.05 level of significance? What does p-value mean?

Question

The owner of Bun ‘N’ Run Hamburgers wishes to compare the sales per day at two locations. The mean number sold for 10 randomly selected days at the Northside site was 83.55, and the standard deviation was 10.50. For a random sample of 12 days at the Southside location, the mean number sold was 78.80 and the standard deviation was 14.25. At the .05 significance level, is there a difference in the mean number of hamburgers sold at the two locations? What is the p-value?

Solution

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Given:

\begin{align*} n_1&=\text{Sample size}=10 \\ n_2&=\text{Sample size}=12 \\ \overline{x}_1&=\text{Sample mean}=83.55 \\ \overline{x}_2&=\text{Sample mean}=78.80 \\ s_1&=\text{Sample standard deviation}=10.50 \\ s_2&=\text{Sample standard deviation}=14.25 \\ \alpha&=\text{Significance level}=0.05 \end{align*}

Given claim: The means differ

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.