Homework SourseAlice bought 100 lottery tickets 15 out of the 100 tickets w
Alice bought 100 lottery tickets. 15 out of the 100 tickets won. Alice thought that the chance of winning is 10%. Can she reject the null hypothesis that the chance of winning is 10% at a 5% significance level?
Alice bought 100 lottery tickets. 15 out of the 100 tickets won. Alice thought that the chance of winning is 10%. Can she reject the null hypothesis that the chance of winning is 10% at a 5% significance level?
Alice bought 100 lottery tickets. 15 out of the 100 tickets won. Alice thought that the chance of winning is 10%. Can she reject the null hypothesis that the chance of winning is 10% at a 5% significance level?
Solution
Ho: p = 10% = 0.1
Ha: p is NOT = 0.1 (two tailed test)
Sample proportion = p^ = 15/100 = 0.15
Standard error of p = SEp = sqrt [p*(1-p)/n]
= sqrt [0.1*0.9/100]
= 0.03
Test statistic = z = [p^ - p] / SEp
= [0.15 - 0.1] / 0.03
= + 1.67
Critical value of z at alpha = 5% is 1.96
Since the test statistic z (1.67) < the critical value of z (1.96), it can be said that there
is NO evidence to reject the Ho.
She cannot reject the Ho.
