Question

A political scientist believes that a given candidate is supported by less than 63% of the votes in the city. He randomly selected a sample of 200 eligible voters in the city and found that only 120 of them declared that they support the candidate. At α = 0.10, is his belief correct?

The null hypothesis is

The alternate hypothesis is

The calculated statistic (leave 4 decimal places only)

The tabulated statistic

Decision if you will reject Ho or you will not reject H0

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.63

Ha : p < 0.63

n = 200

x = 120

= x / n = 120 / 200 =0.60

P0 = 0.63

1 - P0 = 1 - 0.63 =0.37

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.60 - 0.63 / [(0.63*0.37) / 200]

= -0.8787

Test statistic = z =-0.8787

P(z < -0.8787) = 0.1898

P-value = 0.1898

= 0.10

P-value >

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that