The problem I was asked to solve involves a chip company that is rolling out a new flavor across 8 regions in the United States. They want to assess if penetration of these chips is consistent across the regions. The inserted pictures show the data set from a random sample of stores in each region, checking if they carry the new product.
1) Use descriptive statistics to summarize the data from the study. Based on your descriptive statistics, what are your preliminary conclusions about penetration of the chips in grocery stores across the 8 US sales regions?
2) Use the data from the study to test the hypothesis that the proportion of grocery stores that currenty carries the chips is equal across the sales regions. Use [imath]\alpha=0.05[/imath].
3) Do the resuls of your hypothsis test provide evidence that penetration differs across the 8 regions? In which sales region(s) is penetration higher or lower than expected? Use the Marascuillo pairwise comparison at [imath]\alpha=0.05[/imath] to test for differences between regions.
My work:
This is the calculations for the proportions of yes and no stores in the given data sets. I found that across the data, the mean is .7 and the standard deviation is 0.1329607891. The data has a skew of -1.321875246. My answer for #1 is that given the large skew of the data, the penetration is not equal across the different regions.
For #2, I feel that a Chi Square test might be the appropriate way to test the hypothesis, but I'm struggling with how to do that. I think the Chi square might work because I can use it to test the multiple data sets agains what I might have expected had all the proportions been equal.
I'm working with they hypothesis: [math]h_0: p_1=p_2\\h_1: p_1\neq p_2[/math]I'm not sure how to incorporate the fact that there are 8 proportions, not just one - do I just add more [imath]=p_n[/imath] to my hypothesis? And, I'm feeling a little stuck with how to proceed from here.
1) Use descriptive statistics to summarize the data from the study. Based on your descriptive statistics, what are your preliminary conclusions about penetration of the chips in grocery stores across the 8 US sales regions?
2) Use the data from the study to test the hypothesis that the proportion of grocery stores that currenty carries the chips is equal across the sales regions. Use [imath]\alpha=0.05[/imath].
3) Do the resuls of your hypothsis test provide evidence that penetration differs across the 8 regions? In which sales region(s) is penetration higher or lower than expected? Use the Marascuillo pairwise comparison at [imath]\alpha=0.05[/imath] to test for differences between regions.
My work:
This is the calculations for the proportions of yes and no stores in the given data sets. I found that across the data, the mean is .7 and the standard deviation is 0.1329607891. The data has a skew of -1.321875246. My answer for #1 is that given the large skew of the data, the penetration is not equal across the different regions.
For #2, I feel that a Chi Square test might be the appropriate way to test the hypothesis, but I'm struggling with how to do that. I think the Chi square might work because I can use it to test the multiple data sets agains what I might have expected had all the proportions been equal.
I'm working with they hypothesis: [math]h_0: p_1=p_2\\h_1: p_1\neq p_2[/math]I'm not sure how to incorporate the fact that there are 8 proportions, not just one - do I just add more [imath]=p_n[/imath] to my hypothesis? And, I'm feeling a little stuck with how to proceed from here.
