A survey was given to 200 high school students asking their view on the start of

Question

A survey was given to 200 high school students asking their view on the start of the school day. The results of this survey are below. # of Students 72 Like starting before 8 a.m. 116 Would like to start after 8 a.m. 72 Undecided a) Create a 99% confidence interval for the proportion of all high school students that prefer school to start after 8 a.m. Like starting before 8 a.m. Would like school to start after 8 a.m. Undecided b) Create a 90% confidence interval for the proportion of all high school students that prefer school to start after 8 a.m. c) Which interval is wider, the 90% confidence interval or the 99% confidence interval? Why do you think this is true?

Explanation / Answer

a) here sample proportion phat =116/200 =0.58

for n=200

std error =(p(!-p)/n)1/2 =0.0349

fopr 99% CI ; critical value z =2.5758

therfore confidence interval =sample proportion -/+ z*std error =0.4901 ; 0.6699

b)

fopr 90% CI ; critical value z =1.6449

therfore confidence interval =sample proportion -/+ z*std error =0.5226 ; 0.6374

c) from above 99% confidence interval is wider.

as higher confidence interval mean giving greater confidence of having population proportion ; therefore it should be wider to contian population proportion

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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