According to literature on brand loyalty, consumers who are loyal to a brand are
ID: 3238581 • Letter: A
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, 368 Cubs fans among patrons of a restaurant located in Wrigley Ville 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 62.3% of the 138 die-hard fans attended Cubs games at least once a month, but only 20.4% of the 230 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.)
z = __________
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
Let me upload minitab output
n1 = 138, n2 = 230
x1 = 138 * 0.623 = 86
x2 = 230 * .204 = 47
Test and CI for Two Proportions
Sample X N Sample p
1 86 138 0.623188
2 47 230 0.204348
Difference = p (1) - p (2)
Estimate for difference: 0.418841
Test for difference = 0 (vs not = 0):
The test statistics value is Z = 8.53
P Value = 0.000
95% confidence interval for the difference in proportions
95% CI for difference: (0.323, 0.515)
Since p-value = 0.000 < 0.05 and also 95% confidence interval for the difference in proportions does not include zero then we conclude that there is significance difference for the difference in proportions at 5% level od significance.
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