Question

12.52 Christmas Drink.(P576)

In a 2014 nationwide Harris Poll survey about beverage preferences, 195 1 American adults were asked about their preferred beverages during different holidays throughout the year. Overall, 47% of the adults voted for table wine as their preferred beverage for Christmas. Determine and interpret a 95% confidence interval for the proportion, p, of all American adults who prefer wine during holiday

Answer 1

Given,

Number of adults who were asked about their preferred beverages during different holidays throughout the year : Sample size : n= 1951

Percentage of adults voted for table wine as their preferred beverage for Christmas = 47%

Sample Proportion of adults voted for table wine as their preferred beverage: = 47/100 = 0.47

Formula for confidence interval for single population proportions : p

for 95% confidence level = (100-95)/100 = 0.05

/2 = 0.05/2= 0.025

Z_/2 = Z_0.025 = 1.96

95% confidence interval for the proportion , p , of all Americans adults who prefer wine during holiday

95% confidence interval for the proportion , p , of all American adults who prefer wine during holiday = (0.4479, 0.4921)

With 95% confidence we can conclude that the proportion of all American adults who prefer wine during holiday is between 0.4479 and 0.4921

With 95% confidence we can conclude that the percentage of all American adults who prefer wine during holiday is between 44.79% and 49.21%