Question

According to literature on brand loyalty, consumers who are loyal to a brand are likely to consistently select the same product. This type of consistency could come from a positive childhood association. To examine brand loyalty among fans of the Chicago Cubs, 375 Cubs fans among patrons of a restaurant located in Wrigleyville were surveyed prior to a game at Wrigley Field, the Cubs' home field. The respondents were classified as "die-hard fans" or "less loyal fans." Of the 133 die-hard fans, 93.2% reported that they had watched or listened to Cubs games when they were children. Among the 242 less loyal fans, 66.1% said that they watched or listened as children. (Let D = pdie-hard − pless loyal.)

(a) Find the numbers of die-hard Cubs fans who watched or listened to games when they were children. Do the same for the less loyal fans. (Round your answers to the nearest whole number.)

______ die hard fans

______ less loyal fans

(b) Use a one sided significance test to compare the die-hard fans with the less loyal fans with respect to their childhood experiences relative to the team. (Use your rounded values from part (a). Use α = 0.01. Round your z-value to two decimal places and your P-value to four decimal places.)

Z=

P-value=

(c) Express the results with a 95% confidence interval for the difference in proportions. (Round your answers to three decimal places.)

Answer 1

(a)

The  numbers of die-hard Cubs fans who watched or listened to games when they were children is

133 * 0.932 = 123.956

The less loyal fans who watched or listened to games when they were children is

242 * 0.661 = 159.962

124 die hard fans

160 less loyal fans

(b)

Let p1 shows the true proportion of die hard fans who watched or listened to games when they were children and p2 shows the true proportion of less loyal fans who watched or listened to games when they were children.

The test statistics is

z = 5.85

The p-value is: 0.0000

(c)

The required confidence interval is (0.198, 0.344).