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, 380 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 66.7% of the 138 die-hard fans attended Cubs games at least once a month, but only 19.4% of the 242 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.) fans among oast oncea month, but only 19.4%, ohsied P-value 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

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 = 9.21

p - Value = 0.0000

95% confidence interval: (0.380, 0.566)

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. Z-Stat P-value p1 - p2 92.046 138 46.948 242 0.473 0.051377495 9.2063655 <0.0001

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