Question
In: Statistics and Probability
A cellphone provider has the business objective of wanting to estimate the proportion of subscribers who...
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 135 of the
subscribers would upgrade to a new cellphone at a reduced
cost.
a. Construct a 99% confidence interval estimate for the population
proportion of subscribers that would upgrade to a new cellphone at
a reduced cost.
b. How would the manager in charge of promotional programs use the results in (a)?
Solutions
Expert Solution
Solution :
Given that,
n = 500
x = 135
Point estimate = sample proportion = 
= x / n = 135/500=0.27
1 -
= 1-0.27 =0.73
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 =
0.01
/ 2 = 0.01 / 2 = 0.005
Z/2
= Z0.005 = 2.576 ( Using z table )
Margin of error = E = Z
/ 2 * (
* (1 -
)) / n)
= 2.576* (
= 0.0511
A 99% confidence interval for population proportion p is ,
- E < p <
+ E
0.27-0.0511 < p <0.27+ 0.0511
0.2189< p < 0.3211
The 99% confidence interval for the population proportion p is : 0.2189, 0.3211
orchestra answered 1 year agoRelated Solutions
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