Question

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A cable company is planning to offer an improved cable package to its subscribers. Managers are trying to determine the proportion of customers who are likely to purchase the new package to within 5% of the true proportion and want to present their results in a 95% confidence interval. Last time they offered an improved package to their customers, a 95% confidence interval was calculated to be (0.54, 0.64). What is the minimum sample sized needed? A. 363 B. 385 C. 372 D. 382 E. 355

Answer 1

portion estimate is (0.54 + 0.64)/2

1.18/2

0.59

The sample size (n) is calculated according to the formula: n = z² * p * (1 - p) / e²

Where: z = 1.96 for a confidence level (α) of 95%, p = proportion (expressed as a decimal), e = margin of error.

z = 1.96, p = 0.59, e = 0.05

n = 1.96² * 0.59 * (1 - 0.59) / 0.05²

n = 0.9293 / 0.0025 = 371.713

n ≈ 372

The sample size is equal to 372

option c

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