Question

14. A cellphone provider has the business objective of wanting to estimate the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results indicate that 130 of the subscribers would upgrade to a new cellphone at a reduced cost. Complete parts (a) and (b) below. a. Construct a 95% confidence interval estimate for the population proportion of subscribers that would upgrade to a new cellphone at a reduced cost. (Round to four decimal places as needed.) b. How would the manager in charge of promotional programs use the results in (a)? A. The manager can infer that 95% of subscribers that would upgrade to a new cellphone at a reduced cost B. The manager can infer with 95% confidence that the population proportion of all subscribers that would upgrade to a new cellphone at a reduced cost is somewhere in this interval. C. The manager can infer with 95% confidence that the proportion of subscribers in the sample that would upgrade to a new cellphone at a reduced cost is somewhere in this interval. D. The manager can infer that the true population proportion of subscribers that would upgrade to a new cellphone at a reduced cost is somewhere in this interval 95% of the time. 15. If you want to be 99% confident of estimating the population mean to within a sampling error of t3 and the standard deviation is assumed to be 14, what sample size is required? The sample size required is (Round up to the nearest integer.)

Answer 1

Hello

Q - 14 -

(a)

P(1-P) Confidence Interval = P2*1 0.26 + (1 -0.26) Confidence Interval = 0.26 = 1.96*1 500 Confidence Interval = 0.26 (1.96 * 0.0196 Confidence Interval = 0.26 + 0.0384 Confidence Interval = (0.2216,0.2984)

(b) OPTION D

Q - 15 -

$3=2.576*\frac{14}{\sqrt{n}}$

$n=144.49 \approx 144$

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