Question

4. A survey has been conducted to determine what percentage of Canadian tried smoking or had been smoking in their teens (13-19 years old). The survey asked a random sample of Canadians whether they smoked in their teenager years. The data set “S1181 HW5 Q04 Data.xlsx” can be downloaded from D2L.

a) Identify the parameter of interest.

b) Find an approximate 95% confidence interval of the answer from part

(a). Note: Make sure you check necessary conditions.

SUMMARY OF DATA OF SMOKE:

430 "Yes" and 137 "No"

Answer 1

a) Identify the parameter of interest.

p which is popuation proportion of canada   who smoked in their teenager years

b) Find an approximate 95% confidence interval of the answer from part

here n=yes+n=430+137=567

given sample is a random samlpe

and large sample(n>30) follows normal distribution.

we can find confidence interval for p

sample proportion of smoked in their teenager years.=p^=x/n

=430/567

=0.7583774

z alpha/2 for 95%=1.96

95 % confidence interval for p

p^-z*sqrt(p^*(1-p^)/n,p^+z*sqrt(p^*(1-p^)/n

0.7583774-1.96*sqrt(0.7583774*(1-0.7583774)/567,0.7583774+1.96*sqrt(0.7583774*(1-0.7583774)/567

0.7231,0.7936

0.7231<p<0.7936

0.7231*100=72.31%

0.7936*100=79.36%

95% lower limit=72.31%

95% upper limit=79.36%