Question

In: Statistics and Probability

2. A survey of 40 individuals reveals that 19% plan to move within the next year....

2. A survey of 40 individuals reveals that 19% plan to move within the next year. Find a 95% confidence interval for the proportion of people who plan to move next year. (3)

Solutions

Expert Solution

Solution :

Given that,

n = 40

Point estimate = sample proportion = =19%=0.19

1 -   = 1-0.19 =0.81

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 (((0.19*0.81) /40 )

E = 0.122

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.19-0.122 < p < 0.19+0.122

(0.068 , 0.312)

orchestra answered 2 years ago
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