A survey amongst members of a pension scheme asks a stratified random sample of

Question

A survey amongst members of a pension scheme asks a stratified random sample of 250 smokers (out of a total of 5,000 smokers in the pension scheme) and 400 non-smokers (out of a total 10,000 non-smokers): “Do you agree that smoking should be allowed in private cars?” In the sample, 203 of the smokers and 214 of the non-smokers say ‘Yes’. Based on this an estimate, ˆp, of the proportion of all members of the pension scheme who agree that smoking should be allowed in private cars is (to 4 decimal places)

(a) pˆ = 0.6040.

(b) pˆ = 0.6735.

(c) pˆ = 0.6273.

(d) pˆ = 0.6415

I have calculated D. 0.6415 every time, but the answer key says the answer is C.

Explanation / Answer

Since we are here dealing with stratified sampling, we need to check for proportions also.

Proportion of smokers = 5000/15000 = 1/3

Proportion of non smokers = 10000/15000 = 2/3

Hence,

Estimare of proportion of all members of the pension scheme who agree that smoking should be allowed in private cars

= (1/3)*(203/250) + (2/3)*(214/400)

= 0.6273

Option C is correct.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.