Question
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.
Question 1.Use the data in the file to calculate a 98% confidence interval for pF?pM, where pF is the proportion of NC State female students that prefer Diet Coke over Coca-Cola Classic and pM is the proportion of NC State male students that prefer Diet Coke over Coca-Cola Classic. NOTE: calculate the sample proportions to 3 decimal places.
lower bound of confidence interval for pF?pM (round to 2 decimal places).
upper bound of confidence interval for pF?pM (round to 2 decimal places).
Gender = gender of student Drink = drink preference; 0 = Coke Classic, 1 = Diet Coke Gender Drink male 0 female 1 male 1 female 1 male 1 male 1 male 0 female 1 male 1 male 1 female 0 female 1 female 0 male 0 male 0 female 1 female 0 female 1 male 0 male 1 male 0 male 1 male 0 female 1 female 1 female 0 male 1 male 0 male 0 male 1 female 0 female 1 female 1 male 1 female 0 male 0 male 1 male 1 female 1 male 1 female 1 male 0 male 0 female 1 female 1 female 0 male 1 male 1 male 1 female 0 male 1 female 0 female 1 female 1 female 1 female 1 female 0 male 1 male 0 female 1 male 1 female 1 male 0 male 0 female 0 female 0 female 1 male 1 male 1 female 1 female 0 female 1 male 0 female 0 male 0 female 1 male 0 female 1 female 1 female 0 female 0 male 0 male 0 female 0 female 1 male 0 male 0 female 1 male 0 female 1 female 1 male 1 male 1 male 0 male 0 male 1 female 0 male 0 male 0 male 1 male 1 male 1 male 1 female 1 male 0 male 1 male 0 male 0 female 1 male 0 female 1 male 0 male 0 female 1 female 1 female 1 female 1 male 1 female 0 female 1 female 1 female 1 male 1 female 1 male 1 female 0 male 1 female 1 male 1 female 1 female 1 male 0 female 1 male 0 female 0 male 0 male 1 female 1 female 0 male 1 female 1 male 1 male 1 male 0 female 1 female 1 male 0 male 0 male 0 male 0 female 1 male 0 male 0 female 1 female 1 male 0 male 0 female 0 male 0 male 0 female 1 male 1 female 1 male 1 female 0 male 1 female 0 female 1 female 0 male 0 female 0 male 0 male 0 female 0 male 0 female 1 male 0 male 1 male 0 male 0 female 0 female 0 male 0 female 1 female 1 male 1 female 0 female 1 female 0 male 1 male 0 male 1 male 0 male 1 male 1 female 0 male 0 female 1 male 0 female 1 male 1 male 0 female 1 female 0 male 1 female 0 female 1 male 0 male 1 male 1 male 0 male 1 female 1 male 1 female 0 male 0 female 1 female 1 male 0 female 1 male 0 male 0 male 0 male 0 female 0 male 1 male 1 male 0 male 0 female 1 female 1 male 1 male 0 female 1 male 0 female 1 female 0 male 1 male 0 female 1 male 1 female 1 female 1 male 1 male 0 male 1 male 0 female 1 male 1 female 0 female 1 male 0 male 1 male 0 male 1 female 1 male 0 male 0 male 0 male 1 male 0 female 0 male 1 male 0 male 1 female 0 male 0 male 1 female 1 female 1 female 0 male 0 male 0 female 0 male 1 female 0 male 1 female 1 male 0 male 0 male 0 female 1 male 0 female 1 male 0 female 1 female 1 female 1 male 0 male 0 female 1 male 0 male 1 male 0 female 1 female 0 female 1 male 0 male 1 male 1 male 1 female 0 male 0 female 1 female 1 male 0 female 1 female 1 male 0 male 0 male 0 female 1 male 0 female 1 female 1 female 0 female 0 female 0 male 0 female 1 male 1 male 1 female 1 male 0 male 0 male 1 female 1 female 0 female 1 female 0 male 0 male 1 female 1 female 1 male 0 male 1 male 1 female 1 female 1 male 1 female 1 female 0 female 1 male 1 female 0 female 0 female 1 female 1 male 0 female 1 male 0 female 1 male 1 male 0 male 0 female 0 female 1 female 0 male 1 male 1 male 1 male 0 male 1 female 1 female 0 female 1 male 1 male 0 male 0 male 0 female 1 male 1 male 0 male 0 male 1 male 0 female 1 female 0 female 1 male 1 male 0 female 0 female 1 male 1 female 0 male 1 male 1 male 0 female 1 female 1 male 0 male 0 female 1 female 0 female 1 female 1 female 1 male 0 male 0 female 1 female 1 female 1 female 1 female 0 female 0 male 1 male 0 male 1 female 1 female 1 female 1 male 0 female 1 female 0 male 1 male 0 male 1 female 1 female 1 male 0 female 0 female 1 male 1 male 1 female 1 male 0 female 0 female 0 female 1 male 1 male 0 male 0 female 0 male 0 female 0 male 1 male 1 female 0 female 0 male 0 female 0 female 1 female 0 male 1 female 0 male 1 female 0 male 1 male 0 female 1 female 1 female 0 female 0 male 0 male 1 male 1 female 1 male 1 female 0 male 0 female 1 female 1 male 1 female 0 female 1 female 1 female 1 female 0 male 0 female 1 female 1 male 0 female 1 female 0 male 0 male 0 male 0 male 1 male 1 female 0 female 1 female 1 female 1 male 0 female 0 male 1 female 1 male 0 female 1 female 1 female 0 female 0 male 0 male 0 female 1 male 1 male 0 male 0 female 0 female 0 male 1 female 0 female 0 male 1 female 1 male 0 male 1 male 1 male 1 female 1 female 1 male 0 male 1 male 0 female 0 male 0 female 0 male 0 female 1 male 0 male 0 male 1 male 1 female 1 female 1 male 0 male 1 female 0 female 1 female 1
Explanation / Answer
p = (p1 * n1 + p2 * n2) / (n1 + n2)
=(0.638*254+0.442*276)/(254+276)
0.53590
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
=SQRT(0.5359*(1-0.5359)*(1/254+1/276))
0.043362
alpha= 2%
z(a/2) = z(0.02/2) 2.326
CI = (p1-p2) +- z(a/2)*SE
lower =(0.638-0.442)-2.3263*0.043362= 0.10
upper =(0.638-0.442)+2.3263*0.043362= 0.30
sample A sample B x 162 122 n 254 276 p =x/n 0.638 0.442
