Question

Please use all 5 places of decimal when working with probabilities and please use at least 3 significant figures when dealing with proportions. For larger numbers, please use two places of decimal.

A random sample of 500 potential donors were sent invitations to donate to a Birthday Fundraiser on Facebook. 15 persons donated. A random sample of 700 persons were approached to donate to the same cause on GoFundMe. 20 persons donated. Using a 95% confidence interval, test the hypothesis that donation rates are same across both platforms.

Answer 1

Given data are sample,n1=500

And sample proportion p1' = x/n =15/500 = 0.03

Then q1'= 1-p1' = 0.97

n2=700 &

P2'=20/700=0.0286 & q2'= 0.9714

At 95% confidence from z table in 2 tail we have z= 1.96

Null hypothesis is:- H0: p1-p2 = 0

The 95% confidence interval for p1-p2 is =(P1' - p2' )+- E

Where E= margin of error = z √( (p1'q1'/n1) + (p2'q2'/n2) )

E=1.96 × √ ( (0.03 × 0.97 / 500) + ( 0.0286 × 0.9714 / 700) )

E=1.96×0.00989

=0.019392= 0.01939

Then Lower limit is =( p1'-p2') - E

= (0.03 - 0.0286) - 0.01939

=0.0014 - 0.01939 = -0.01799

Upper limit is = (p1'-p2') + E

=(0.03- 0.0286) + 0.01939

=0.0014 + 0.01939 =0.02079

So the 95% confidence interval for p1-p2 is ( -0.018 , 0.021)

Decision :- Then 0 is with in the 95% confidence interval

so fail to reject the null hypothesis H0

conclusion :- At 95% confidence donation rates are same across both platforms