According to literature on brand loyalty, consumers whoare loyal 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, 365 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 134 die-hard fans, 88.1%reported that they had watched or listened to Cubs games when theywere children. Among the 231 less loyal fans, 71.0% said that theywatched or listened as children. (Let D =pdie-hard ? plessloyal.)
(a) Find the numbers of die-hard Cubs fans who watchedor listened to games when they were children. Do the same for theless loyal fans. (Round your answers to the nearest wholenumber.)
| die-hard fans |
| less loyal fans |
(b) Use a one sided significance test to compare thedie-hard fans with the less loyal fans with respect to theirchildhood experiences relative to the team. (Use your roundedvalues from part (a). Use ? = 0.01. Round yourz-value to two decimal places and your P-value tofour decimal places.)
Conclusion
____Reject the null hypothesis, there is 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.
____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 not 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 forthe difference in proportions. (Round your answers to three decimalplaces.)
( ______ , ______ )
Thank you
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