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, 391 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 69.9% of the 136 die-hard fans attended Cubs games at least once a month, but only 18.0% of the 255 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.)

Explanation / Answer

Sol:

Ho:p1=p2

H1: p1 not =p2

alpha=0.05

CALCULATION:

(p1^-p2^)+-Z critsqrt(p1^(1-p1^/n1+p2^(1-p2^)n2

z crit for 95%=1.96

0.699-0.18)+-1.96sqrt(0.699(1-0.699)/136+0.18(1-0.18)/255)

=0.519+-0.0904

=0.519-0.0904,0.519+0.0904

=0.4286,0.6094

lower limit=0.429

upper limit=0.609

0.429<p1-p2<0.609

The confidence inetrval does not contain zero.

Reject Null hypothesis.

Accept Alternative Hypothesis,

there is sufficient statistical evidence at 5% level of signiifcance through confidence intervals to conclude that

for the difference in proportions.

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