Question

A large study of adults over the age of 70 was conducted. There were 4989 whites and 906 blacks included in the study.

The researchers asked about medical conditions associated with the elderly (such as stroke, cancer, heart disease, hypertension. etc.) and about any difficulty the subjects had with the activities of daily living. 529 of the 4989 elderly whites reported having had a stroke, and 103 of the 906 elderly blacks reported having had a stroke.

(a) Compute the incidence (sample proportion) of stroke among of elderly whites ________________  

(b) Compute the incidence (sample proportion) of stroke among of elderly blacks ________________

(c) We want to know if the difference in the proportion p₁ of elderly whites and p₂ of elderly blacks who experience a stroke is statistically significant at the significance level is 0.05.

State the null hypothesis: H₀: p₁ ____ p₂

State the alternative hypothesis: (Is there a difference?) H_a: p₁ ____ p₂                     

Test statistic ___________________              p-value __________________        

         

Is the difference significant? ___________________                                                                                                         

                                                                      Yes or no

Answer 1

Part a)

Part b)

Part c)

To Test -

H0 :- P1 = P2

H1 :- P1 P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 529 + 103 ) / ( 4989 + 906 )
= 0.1072

Z = -0.69

Test Criteria :-
Reject null hypothesis if

= -0.69 > -1.96, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < -0.69 )
P value = 0.4902
Reject null hypothesis if P value <
Since P value = 0.4902 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Is the difference significant, NO