According to literature on brand loyalty, consumers who are loyal to a brand are

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, 371 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." The study found that 67.4% of the 135 die-hard fans attended Cubs games at least once a month, but only 21.2% of the 236 less loyal fans attended this often. Analyze these data using a significance test for the difference in proportions. (Let D = pdie-hard pless loyal. Use = 0.05. Round your value for z to two decimal places. Round your P-value to four decimal places.)

Analyze these data using a 95% confidence interval for the difference in proportions. (Round your answers to three decimal places.)

  ,

Write a short summary of your findings.

a) Reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month.

b) Fail to reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month.   

c) Reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month.

d) Fail to reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month.

z = P-value =

Explanation / Answer

The statistical software output for this problem is:

Two sample proportion summary hypothesis test:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 0

Hypothesis test results:

95% confidence interval results:

Hence,

z = 8.82

p - Value = 0.0000

95% confidence interval: (0.367, 0.557)

Summary: Reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month.

Option C is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 90.99 135 50.032 236 0.462 0.052381356 8.819932 <0.0001

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