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 110 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.
Solutions
Expert Solution
Solution :
Given that,
n = 500
x = 110
Point estimate = sample proportion = 
= x / n = 110/500=0.22
1 -
= 1- 0.22 =0.78
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.96 ( Using z table )
Margin of error = E = Z
/2 *
* (1 -
)) / n)
= 1.96 (
E = 0.0363
A 95% confidence interval for population proportion p is ,
- E < p <
+ E
0.22- 0.0363< p <0.22+ 0.0363
0.1837< p < 0.2563
The 95% confidence interval for the population proportion p is : 0.1837,0.2563
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