To compare the effect of weather on sales of soft drinks, a distributor surveyed

Question

To compare the effect of weather on sales of soft drinks, a distributor surveyed people in two regions of the country and asked if they purchased soft drinks in the last month. The following are the results. The distributor would like to know if there is a difference in sales between the two regions. Region A Region B Sample size Number who purchased 1000 400 1500 500 a. What is the null hypothesis and the alternate hypothesis? b. What is the proportion of people who purchased soda in Region A? c. What is the proportion of sales made in Region B? d. What is the pooled (or weighted average) estimate of the population proportion? e. Using the 1% level of significance, what is the critical value? f. What is the value of the test statistic? g. Test the hypothesis with a 0.01 significance level. What is our decision?

Explanation / Answer

We use here two sampleproportion test to compate effect of weather on sales of soft drinks.

using Minitab:

Test and CI for Two Proportions

Sample X N Sample proportion
1 400 1000 0.400000................................proportion of person who purchased soda in Region A
2 500 1500 0.333333................................proportion of person who purchased soda in Region B

Difference = p (1) - p (2)
Estimate for difference: 0.0666667
99% CI for difference: (0.0159190, 0.117414)
Test for difference = 0 (vs not = 0): Z = 3.40 P-Value = 0.001

Fisher's exact test: P-Value = 0.001

Critical t value =+-2.57

The decision rule is: Reject H0 if Z < -2.57 or if Z > 2.57 so here we reject the null hypothesis.

Hope this helps you. Thanksa nd God bless you :-)

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