Bimble, as a statistical analyst at her company, has been asked to find out the

Question

Bimble, as a statistical analyst at her company, has been asked to find out the customer satisfaction rate of the company's new product. The satisfaction rate for the older product has been known that 73% of customers are satisfied with the older product. Her company wants to ensure that customers will have higher satisfaction rate with the new product so that the company can confidently claim this in their advertisement. As the true customer satisfaction rate for the new product is still unknown, in order to uncover the truth, Bimble took a simple random sample of 250 customers and found that 193 of them reported that they were satisfied with the new product.

a) Bimble runs into the company's CEO and needs to make a quick report on the new product. What will be her point estimate of the new product's true customer satisfaction rate (i.e population proportion?)

b) Now Bimble has more time and wants to be more confident in her estimation to report to the CEO. Help Bimble construct 95% Confidence Interval for the true customer satisfaction rate (population proportion ) of the new product.

Explanation / Answer

(a)

Point estimate of population proportion = Sample proportion (p_bar) = 193 / 250 = 77.2%

(b)

Value of Z at 95% confidence interval (two-tailed) = NORMSINV(1 - (1 - 0.95)/2) = 1.96

Estimate for the standard error (Sp) = SQRT(p_bar *(1 - p_bar) / N) = SQRT(0.772*(1 - 0.772)/250) = 0.0265

So, the cofidence interval is:

p_bar +/- z*Sp

= 0.772 +/- 1.96*0.0265 or, [72%, 82.4%]

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