Answer:
The correct option is d.
Step-by-step explanation:
The formula for confidence interval for the actual proportion in the population is
[tex]CI=p\pm z^*\sqrt{\frac{p(1-p)}{n}}[/tex]
Where, p is population proportion, n is sample size and z* is the tabulated value of z at given confidence interval.
The value of z* is 3 for 99.7% confidence interval.
[tex]CI=0.65\pm 3\times \sqrt{\frac{0.65(1-0.65)}{30}}[/tex]
[tex]CI=0.65\pm 3\times \sqrt{\frac{0.65(0.35)}{30}}[/tex]
[tex]CI=0.65\pm 0.261247[/tex]
[tex]CI=[0.65-0.261247,0.65+0.261247[/tex]
[tex]CI=[0.388753,0.911247][/tex]
[tex]CI=[0.389,0.911][/tex]
Therefore the 99.7% confidence interval for the actual proportion in the population is between 0.389 and 0.911. Option d is correct.
