1) A retail store would like to compare sales from two different arrangements of displaying its merchandise. Sales are recorded for a 30 day period with one arrangement and then sales are recorded for another 30 day period with the alternative arrangement. Would the data for each of the two 30 day periods be independent or dependent? Why so?
2) A random sample results in 1 = 20 with n1 = 100. The population standard deviation is σ1 = 6. Another sample was selected independently resulting in 2 = 22 with n2 = 100. The population standard deviation is σ2 = 7. Test that the population means differ using a 1% significance level.
3) The observations below resulted from independent random samples selected from approximate normal populations:
Sample 1: 4.5, 7.0, 3.1, 6.2, 5.8, 6.1
Sample 2: 6.5, 5.4, 7.8, 8.1, 7.9
a) Conduct a test of hypothesis to determine if the mean of the second population is greater than the mean of the first population. Assume that the population variances are equal. Use a .05 significance level.
b) Perform the statistical test in part a) but do not assume that the population variances are equal.
4) Twenty mortgage firms were selected and the amount of mortgage financing was recorded for 2010 and 2011. If the mean difference was $5.434 million with the standard deviation of the differences being $8.764 million, is there sufficient evidence to support that a difference exists in the amount of mortgage refinancing for 2010 and 2011? Use a 1% significance level.
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