The question that was asked, "Which of the following three products are you most interested in?" Then the results were tallied, indicating how many males and how many females preferred each of the three options. A study for each collected the following data. Test for independence at a significance of 5%. 1) What are your conclusions and how would you recommend the results be used by the marketing department?

Categories 50 Over 50 years or younger Low sodium 31 40 Regular broth 33 38 Creamed 36 22 soupsCategories Male Female Low calorie 12 46 Regular broth 22 32 Creamed soups 66 221) Using the information provided we can state the hypothesis: HO: Gender and low-calorie product preferences are independent Ha: Gender and low-calorie product preferences are dependent Significance level: cc = 0.05 We organize the observed data and calculate the expected. After which, use the Chi Square formula: X2: ngs OBSERVED EXPECTED CHI SQUARE CATEGORIES Male Female Column Categories Male Female Column Categories Male Female Column Total Total Total LOW 12 45 58 LowI Calorie 29 29 58 LowI Calorie 9.9? 9.9? 19.93 CALORIE REGULAR 22 32 54 Regular 2? 2? 54 Regular 0.93 0.93 1.85 BRO'I'H Broth Broth CREAMED 66 22 88 Creamed 44 44 38 Creamed 11 11 22 SOUPS Soups Soups ROW TOTAL 100 100 200 Row Total 100 100 200 Row Total 21.89 21.89 43.78 From the Chi-Square table the value for d, and significance of 5% Chi Square Critical Value gins): 5.991 Chi Square Statistic g4; ) = 43 .78 Chi Square Statistic (43 .78) > Chi Square Critical Value (5.991) Reject HO. So, we will work under the alternative hypothesis, which suggests that gender and low-calorie products are dependent. 2) Using the information provided we can state the hypothesis: HO: Age and low-calorie product preferences are independent Ha: Age and low-calorie product preferences are dependent Significance level: (1 = 0.05 We organize the observed data and calculate the expected. After which, use the Chi Square formula: X2: ZmgEV OBSERVED EXPECTED CHI SQUARE CATEGORIES 50 Years or Over Column Total Categories 50 Years or Over Column Total Categories 50 Years or Over Column Younger 50 Younger 50 Younger 50 Total LOW 31 40 71 Low 35.5 35.5 71 Low 0.57 0.5? 1.14 CALORIE Calorie Calorie REGULAR 33 38 71 Regular 35.5 35.5 71 Regular 0.28 0.18 0.35 BROTH Broth Broth CREAMED 35 22 58 Creamed 29 29 58 Creamed 1.69 1.59 3.38 SDUPS Soups Soups ROW TOTAL 100 100 200 Row Total 100 100 200 Row Total 2.44 2.44 4.87 From the Chi-Square table the value for d, and significance of 5% Chi Square Critical Value (King 5.991 Chi Square Statistic Li: ) = 4.87 Chi Square Statistic (4.87) 4. Chi Square Critical Value (5.991) Accept HO. So, we will work under the null hypothesis, which suggests that age and low-calorie products are independent