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, 374 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 132 die-hard fans, 93.9%reported that they had watched or listened to Cubs games when they were children. Among the 242 less loyal fans, 67.8% said that they watched or listened as children. (Let D = p_die-hard − p_{less 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	= _______

Conclusion

Fail to reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

Reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.     

Reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

Fail to reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

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

( _______, _______ )

Answer 1

Given: For die hard fans : n1=132 , p1=93.9%=0.939

For less loyel fans : n2=242 , p2=67.8%=0.678

The pooled estimate is given by,

Q=1-P=0.2299

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

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

(b) Hypothesis : Vs

The test statistic is ,

P-value =

Decision : Here , P value = 0.0000 <

Therefore , reject the null hypothesis

Conclusion : there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children.

(c) The 95% confidence interval for the difference in proportions is ,