In: Statistics and Probability
A brand of refrigerators, denoted A is guaranteed for 1 year. In a random sample of 50 refrigerators of brand A, 12 were observed to fail before the guarantee period ended. Estimate the true proportions of failures during the guarantee period, with 98% confidence interval. State the conclusion sentence and find the point estimator for the population proportion
Solution :
Given that,
n = 50
x = 12
Point estimate = sample proportion = = x / n = 12 / 50 = 0.24
1 - = 1 - 0.24 = 0.76
At 98% confidence level
= 1 - 98%
=1 - 0.98 =0.02
/2
= 0.01
Z/2
= Z0.01 = 2.326
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.326 (((0.24 * 0.76) / 50)
= 0.140
A 98% confidence interval for population proportion p is ,
± E
= 0.24 ± 0.140
= ( 0.100, 0.380 )
We are 98% confident that the true proportion of failures during the guarantee period between 0.100 and 0.380.