In a marketing survey, a random sample of 740 women shoppers revealed that 625 r

Question

In a marketing survey, a random sample of 740 women shoppers revealed that 625 remained loyal 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 Institute.) Let p represent the proportion of all women shoppers who remain loyal to their favorite supermarket. a) Is the normal approximation valid? Explain. 2. Department, Food Marketing yes/ n- b) Find and interpret a 95% confidence interval for p.

Explanation / Answer

a) Yes, a normal approximation is valid as according to central limit theory as more and more samples are takes, the normal approximation becomes more valid. Since. n = 740 >> 30 , we can assume normality

b) CI = x +- zvalues * SEof mean

Here p = 625/740 = 0.84446

Also z-value for a 95% confidence interval = 1.96

SE of mean = 1/sqrt(740) = 0.037 ( We take Std deviation of sample as 1 as it is a normal and no SD is given)

CI = 0.84446 +- 1.96*0.037 = (0.7724, 0.9165)

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