2. In a to their favorite supermarket during the past year (i.e. did not switch

Question

2. In a to their favorite supermarket during the past year (i.e. did not switch stores.) (Source: Trends in the United States: Consumer Attitudes and the Supermarkets, the Research Department, Food Marketing Institute.) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. a) Is the normal approximation valid? Explain. marketing survey, a random sample of 740 women shoppers revealed that 625 remained loyal b) Find and interpret a 95% confidence interval for p.

Explanation / Answer

a)

Yes, normal approximation is valid

Verify whether n is large enough to use the normal approximation by checking the two appropriate conditions.

1. n?p = 625

2. n?(1 – p) = 740 - 625 = 115

In order to use normal approximation both np and n(1-p) should be at least 10

b)

CI for 95%

n = 740

p = 625/740 = 0.8446

z-value of 95% CI = 1.9600

SE = sqrt(p*(1-p)/n)

= sqrt(0.8446*(1-0.8446)/740)

= 0.01332

ME = z*SE

= 1.96*0.01332

= 0.02610

Lower Limit = p - ME = 0.8446 - 0.0261 = 0.81849

Upper Limit = p + ME = 0.8446 - 0.0261 = 0.87070

95% CI (0.8185 , 0.8707 )

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