Answer:
95% confidence interval for the percentage of students who change their major
(0.69881 , 0.86119)
Step-by-step explanation:
Step(i):-
Given that the sample size 'n' = 100
Given that the sample proprtion
p = 78% = 0.78
Level of significance =0.05
Critical value Z₀.₀₅ = 1.96
Step(ii):-
The 95% of confidence interval is determined by
[tex](p^{-} -Z_{0.05} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p^{-} +Z_{0.05} \frac{\sqrt{p(1-p)} )}{\sqrt{n} })[/tex]
[tex](0.78 - 1.96 \frac{\sqrt{0.78(1-0.78)} }{\sqrt{100} } , 0.78 +1.96 \frac{\sqrt{0.78(1-0.78} )}{\sqrt{100} })[/tex]
(0.78 - 0.08119,0.78 + 0.08119 )
(0.69881 , 0.86119)
Final answer:-
95% confidence interval for the percentage of students who change their major
(0.69881 , 0.86119)
