According to literature on brand loyalty, consumers who areloyal to a brand are likely to consistently select the sameproduct. This type of consistency could come from a positivechildhood association. To examine brand loyalty among fans of theChicago Cubs, 374 Cubs fans among patrons of a restaurant locatedin Wrigleyville were surveyed prior to a game at Wrigley Field, theCubs' home field. The respondents were classified as \"die-hardfans\" or \"less loyal fans.\" Of the 132 die-hard fans, 93.9%reportedthat they had watched or listened to Cubs games when they werechildren. Among the 242 less loyal fans, 67.8% said that theywatched or listened as children. (Let D =pdie-hard − plessloyal.)
(a) Find the numbers of die-hard Cubs fans who watched orlistened to games when they were children. Do the same for the lessloyal 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 fanswith the less loyal fans with respect to their childhoodexperiences relative to the team. (Use your rounded values frompart (a). Use α = 0.01. Round your z-value to twodecimal places and your P-value to four decimalplaces.)
| z | = _______ |
| P-value | = _______ |
Conclusion
Fail to reject the null hypothesis, there is not significantevidence that a higher proportion of die hard Cubs fans watched orlistened to Cubs games as children.
Reject the null hypothesis, there is significant evidence that ahigher proportion of die hard Cubs fans watched or listened to Cubsgames as children.    Â
Reject the null hypothesis, there is not significant evidencethat a higher proportion of die hard Cubs fans watched or listenedto Cubs games as children.
Fail to reject the null hypothesis, there is significantevidence that a higher proportion of die hard Cubs fans watched orlistened to Cubs games as children.
(c) Express the results with a 95% confidence interval for thedifference in proportions. (Round your answers to three decimalplaces.)
