Traditional mass marketing of a single product has given way

Traditional mass marketing of a single product has given way to target marketing which focuses on satisfying the demands of a particular segment of a product\'s market.

To appeal to the various segments of the soft-drink-related market, the Coca Cola Company\'s products include Coca Cola Classic, Caffeine-Free Coke, Diet Coke, Caffeine-Free Diet Coke, Coke Zero, Cherry Coke, Diet Cherry Coke, Mello-Yello, Sprite, Powerade, Powerade Zero, Smart Water, Vitamin Water, Minute-Maid Orange Juice, and others. Each of these Coca-Cola products is meant to appeal to a different market segment when a consumer desires a non-alcoholic beverage.

As part of an effort to improve and refine their marketing program directed toward NC State students, the Coca Cola Company needs to estimate the difference between the proportion of female students and the proportion of male students that prefer Diet Coke when the choice is between Diet Coke and Coca Cola Classic.

The Coca Cola Company selects a random sample of 530 NC State students and records the gender of each student along with each student\'s preference of Coco-Cola Classic or Diet Coke. The results are in this Excel file (http://www.webassign.net/userimages/coke%20diet%20coke%20preference%20survey.xls?db=v4net&id=283245).

Question 1.Use the data in the file to calculate a 95% confidence interval for p_F?p_M, where p_F is the proportion of NC State female students that prefer Diet Coke over Coca-Cola Classic and p_M is the proportion of NC State male students that prefer Diet Coke over Coca-Cola Classic.

_____ lower bound of confidence interval for p_F?p_M (round to 2 decimal places).
_____ upper bound of confidence interval for p_F?p_M (round to 2 decimal places).

Solution

Cross table of the data

       female male All

0          92   154 246

1         162   122 284

All       254   276 530

Question 1.Use the data in the file to calculate a 95% confidence interval for p_F?p_M, where p_F is the proportion of NC State female students that prefer Diet Coke over Coca-Cola Classic and p_M is the proportion of NC State male students that prefer Diet Coke over Coca-Cola Classic.

0.11 lower bound of confidence interval for p_F-p_M (round to 2 decimal places).
0.28 upper bound of confidence interval for p_F-p_M (round to 2 decimal places).

p_{F =162/254   =0.6378}

p_{M =122/276 =0.442}

Group 1 Proportion

0.6378

Group 2 Proportion

0.4420

Difference in Two Proportions

0.1958

Confidence Level

95%

Intermediate Calculations

Z Value

1.9600

Std. Error of the Diff. between two Proportions

0.0425

Interval Half Width

0.0832

Confidence Interval

Interval Lower Limit

0.1125

Interval Upper Limit

0.2790