In: Math
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, 365 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 134 die-hard fans, 88.1% reported that they had watched or listened to Cubs games when they were children. Among the 231 less loyal fans, 71.0% 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 | = |
Conclusion
____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.
____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.
____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 not 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.)
( ______ , ______ )
Thank you
,
a) Number of die-hard Cubs fans who watched or listened to games when they were children
Number of less loyal fans who watched or listened to games when they were children
b)
Conclusion : 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)