Question

In: Math

a random sample of 175 xray machines is taken. and 54 machines in the sample malfunction....

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

Expert Solution

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} * $\sqrt$ (( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((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

milcah answered 1 year ago

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