Question 1 3+2+10Marks (a) Isthere any Relationship between confidence interval

Question

Question 1                                                                                               3+2+10Marks

(a) Isthere any Relationship between confidence interval and tests ofHypothesis?

      Justify your answer.

(c) In arandom sample of 200 persons having their lunch at the Universitycafeteria on meatless day it was observed that 30 percent preferredvegetable dishes.

i.         Find 95%confidence interval for p.

ii.       How large a sample isneeded if we want to be 95% confident that our estimate ofp is within 0.02?

Explanation / Answer

Moment generating function for the normal distribution isMx(t) =mt+ (s2t2)/2

Mean of moment generating function of normal distribution is[d[Mx(t)]/dt]t=2=[m+(s2t/2)]t=2   

Here n=200;

Vegetarian percentage=30% in 200=60

Vegetarian Proportion p= 60/200=0.3

Therefore q=1-p=0.7

Here Ho: p=0.5 H1=!0.5

Test for single proportion Z=p^-P/Öpq/n

                                        Z=0.3-0.5/Ö(0.3*0.7)/200

                                        Z=-15.1303

For Z-alpha vale at 95% level of significance=1.96

95% confidence interval =p^-Za*Öpq/n<P<p^+Za*Öpq/n

                                        0.3-1.96*0.32404<P<0.3+1.96*0.32404

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

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