Question

Judging on the basis of​ experience, a politician claims that 52​% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed20randomly selected people in that​ area, and14 of them reported having voted for an independent candidate. The null hypothesis is that the overall proportion of voters in the area that have voted for an independent candidate is 52​%.What value of the test statistic should you​ report?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.52

Ha : p 0.52

= x / n = 14/20 = 0.70

P0 = 0.52

1 - P0 = 1 - 0.52 = 0.48

Test statistic = z

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

= 0.70 - 0.52 / [0.52*(0.48) / 20]

= 1.611

P(z > 1.611 ) = 1 - P(z < 1.611 ) = 0.1071

P-value = 0.1071