Question

A market research company conducted a telephone survey of 320 Melbourne households to determine the proportion of households seeking to purchase a new car in the next two years. An interval estimate of 0.134 to 0.196 was calculated. Determine the level of confidence (answer as percentage correct to two decimal places).

Answer 1

in the question sample size = 320

interval estimate is given as 0.134 - 0.196

interval estimate = point estimate +or - critical value * standard error

the difference between the intervals = 0.196 - 0.134

= 0.062

therefore critical value * standard error = 0.062/2

= 0.031

point estimate = 0.196 - 0.031

= 0.165

for population proportion standard error = square root of (P*Q/N) where P is the probability of success, Q =probability of  failure and N= sample size

N = 320

Probability of success, P = 0.165 and

probability of failure, Q = 1 - P = 0.835

in this question std. error = square root of ( (0.165*0.835)/ 320)

= square root of (0.137775/320)

= 0.020749023

critical value*std. error = 0.031

therefore critical value = 0.031/ std. error

= 0.031/0.020749023

= 1.494

from the t table (statistical tables) the confidence value corresponding to the critical vale 1.494 is 0.9319.

therefore the level of confidence is 93.19%