# How to calculate 95% confidence interval of two group means and perform hypothesis test comparing group means?

Below is the information about the weight of coffee (in thousand kg) sold at two locations (location1 and location 2)

26.3, 26.5, 16.2, 16.2, 26.4, 16.8, 16.1, 16.9 (8 shops)
44.4, 44.7, 34.9, 54.1, 44.8, 22.6, 36.4 (7 shops)

1. Find the 95% confidence interval for the difference between the mean weight for the coffee sold at different locations.
2. where do you prefer to own a shop? Why? Explain
3. Now you need to prove whether preferred area has really got higher mean of weight of coffee sold over the week in question. carry out appropriate tests at 5% and 1% levels.
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Since this is homework, it is very important that you show us what you've tried to do to solve it. –  Zen Jun 24 '12 at 5:31

Assuming the first 8 shops are at location 1 and the next 7 at location 2 you can do a two sample t test. It appears that the differences in weight is large and will be significant at both the 5% and 1% levels but that should be determined by calculating the test statistic and comparing it to the critical value for a t distribution with 8+7-2=13 degrees of freedom. If it appears that the samples do not come from normal distributions then the Wilcoxon rank sum test could be applied.

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