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, 366 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 64.5% of the 138 die-hard fans attended Cubs games at least once a month, but only 21.5% of the 228 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

here p1 =0.645 ; n1=138

p2=0.215 ; n2 =228

std error of the difference =(p1(1-p1)/n1 +p2(1-p2)/n2)1/2 =0.049

hence test stat z=(p1-p2)/std error =8.7782

for above p value =0.0000

as p value is significantly less then 0.05 ; there is significant difference in proportion

for 95% CI, z=1.96

hence confidence interval =(p1-p2) +/- z*std error =0.334 ; 0.526

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