Question

A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.

(1). The test statistic is

1. 0.80
2. 0.05
3. 1.25
4. 2.00

(2). The p-value is

a.      0.2112

b.      0.05

c.      0.025

d.      0.1056

(3). At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A

      a.         is significantly greater than 80%

      b.         is not significantly greater than 80%

      c.         is significantly greater than 85%

      d.         is not significantly greater than 85%

Answer 1

To Test :-
H0 :- P = 0.80
H1 :- P > 0.80

P = X / n = 85/100 = 0.85

Test Statistic :-
Z = ( P - P0 ) / √ ((P0 * q0)/n))
Z = ( 0.85 - 0.8 ) / √(( 0.8 * 0.2) /100))
Z = 1.25

Test Criteria :-
Reject null hypothesis if Z > Z(α)
Z(α) = Z(0.05) = 1.645
Z < Z(α) = 1.25 < 1.645, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 1.25 ) = 0.1056
Reject null hypothesis if P value < α = 0.05
Since P value = 0.1056 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

(1). The test statistic is 1.25

(2). The p-value is  

d.      0.1056

(3). At 95% confidence, it can be concluded that the proportion of the population in favor of candidate

b.         is not significantly greater than 80%.