Question

Several years ago the proportion of Americans aged 18 - 24 who invested in the stock market was 0.20. A random sample of 100 Americans in this age group was recently taken. They were asked whether or not they invested in the stock market. The results follow: "Yes" Responses: 49 "No" Responses: 51 At a .05 level of significance, we want to know if the proportion of Americans aged 18 - 24 who invested in the stock market change For this information respond:

a) The Null (Ho) hypothesis is:  

b) The Standard Error of P is  

c) The Test Statistic (Z-test) is  

d) The P-value is:  

e) Do we reject (state yes or no):

Answer 1

To Test :-

H0 :- P = 0.2

H1 :- P   0.2

Standard Error of P =  

n = 100
P = X / n = 49 / 100 = 0.49

Test Statistic :-


Z = 7.25

Test Criteria :-
Reject null hypothesis if

= 7.25 > 1.96, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = 2 * P ( Z > 7.25 )
P value = 0
Reject null hypothesis if P value <
Since P value = 0 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the proportion of Americans aged 18 - 24 who invested in the stock market change.