Question

Solve the following question

(1) Some candidate claims that he will win the election. We did a survey, found that among
2000 voters we surveyed, only 900 would vote for him. Based on the survey, we want to
check whether the candidate will lose the election, we turn this problem as testing problem.
a). Set hypothesis. H0 : p = 0.5, Ha is:
A. p > 0.5, B. p < 0.5, C. p 6= 05, D. p > 0.45, E. p = 0.45.
b). Test statistic is:
A. −3.45, B. −2.89, C. −4.47, D. −1.48, E. −0.78.
c). p-value is
A. 0.000, B. 0.001, C. 0.005, D. 0.015, E. 0.999.
d). Decision is:
A. We can not conclude the candidate will lose the election at α = 0.05.
B. We can conclude the candidate will lose the election at α = 0.01.
C. We can not conclude the candidate will win or will lose the election at α = 0.05.
D. Since p-value very large, so, we can conclude that the candidate lose the election .
E. Based on given information, no clear conclusion can be made.

Answer 1

Solution:

a). Set hypothesis. H0 : p = 0.5, Ha is:

p < 0.5

Option B is correct.

(Because , we want to check whether the candidate will lose the election)

b) First we find sample proportion

= 900/2000 = 0.45

The test statistic z is

z =   

=  (0.45 - 0.5)/[0.5*(1 - 0.5)/2000]

= -4.47

Option C is correct.

c)

Here , < sign in Ha . So left tailed test.

p value = P(Z < -4.47) = 0.0000

Option A is correct.

d)

Decision is:

We can conclude the candidate will lose the election at α = 0.01.

Option B is correct.