# Suppose a market analyst wants to determine the difference in the average price

August 30, 2017

Question
7. Suppose a market analyst wants to determine the difference in the average price if a gallon
of whole milk in Seattle and Atlanta. To do so, he takes a telephone survey of some randomly
selected consumers in Seattle. He then takes another sample of some respondents from Atlanta.
Use the following sample of prices of a gallon of milk in both the cities, solve the following
questions.
Sample 1 Sample 2
Seattle Atlanta
\$2.55 \$2.36 \$2.43 \$2.23 \$2.40 \$2.39
2.67 2.54 2.43 2.30 2.33 2.40
2.50 2.54 2.38 2.19 2.29 2.23
2.61 2.80 2.49 2.41 2.18 2.29
3.10 2.61 2.57
(i)Test the hypothesis that H0: 2
2
2
? 1 = ? against the alternative hypothesis H0: 2
2
2
? 1 ? ? at 5% label of
significance.
(a) What is the point estimate of the difference between the two population mean difference
µ Seattle ? µ Atlanta ?
(b) Test the hypothesis that : 0 H0 µ Seattle ? µ Atlanta = against : ? ? 0 Ha µ Seattle µ Atlanta .
Use 5% level of significance. Show all six steps. Use Classical approach and p-value approach.
8. The following information was obtained from matched samples.
The daily production rates for a sample of workers before and after a training program are shown below.
Worker Before After
1 20 22
2 25 23
3 27 27
4 23 20
5 22 25
6 20 19
7 17 18
Questions:
(i) Estimate the point estimate for the difference between the means of the two populations
µ d =µ A ? µ B .
(ii) Test the null hypothesis H0: µ d ? 0 against Ha µ d : > 0 at 5% label of significance,
(iii) Compute a 95% confidence interval for the difference between the means of the two
populations µ d =µ A ? µ B .

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