Question

In a survey of 4100 ​adults, 732 say they have seen a ghost. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

Answer 1

In a survey of 4100 ​adults, 732 say they have seen a ghost. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

Answer : We have given :

n = sample size = 4100 total

x = 732 say they have seen a ghost

phat = sample proprtion = x / n = 732 / 4100

= 0.1785

α = level of significance = 99 % ie 0.01

# we have to calculate 99 % confidence interval for population proportion : p

P = population proportion  

P = [ phat  ± Z_c * sqrt ( phat * (1 - phat) / n )) ]

Z_c   = critical value for z test = ± 2.58 ( from table )

and

# sqrt ( phat * (1 - phat) / n )) = sqrt ( 0.1785 * (1 - 0.1785 ) / 4100 )) = 0.00598

P = [ phat  ± Z_c * sqrt ( phat * (1 - phat) / n )) ]

= [ 0.1785  ± ( 2.58 * 0.00598) ]

= [ 0.1785 ± 0.0154 ]

= [ 0.1631 , 0.1939 ]

lower limit = 0.1631 and

upper limit = 0.1939

Interpretation :

we can say 99 % confident that population proportion is lies within    0.1631 to   0.1939