Question

a random sample of 175 xray machines is taken. and 54 machines in the sample malfunction. compute a 95% confidence interval for the proportion of all xray machines that malfunction. then calculate the upper and lower limit of the 95% confidence intervals

Answer 1

Solution :

Given that,

n = 175

x = 54

Point estimate = sample proportion = = x / n = 54 / 175 = 0.31

1 - = 1 - 0.31 = 0.69

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.96}

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

= 1.96 (((0.31 * 0.69) / 175)

= 0.069

A 95% confidence interval for population proportion p is ,

± E  

0.31 ± 0.069

0.241 , 0.379

lower limit = 0.241

upper limit = 0.379