Question

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.

Answer 1

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 = 1.282

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.282 (((0.24 * 0.76) / 50)

= 0.077

A 98% confidence interval for population proportion p is ,

± E  

= 0.24  ± 0.077

= ( 0.163, 0.317 )

We are 98% confident that the true proportion of failures during the guarantee period between 0.163 and 0.317.