Question

Judging on the basis of​ experience, a politician claims that 45​% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed 20 randomly selected people in that​ area, and 15 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 ​42% What value of the test statistic should you​ report?

Answer 1

To find the test statistic, we need to use the formula:

z = (p - P) / sqrt[(P * (1 - P)) / n]

where:

p = sample proportion = 15/20 = 0.75

P = hypothesized population proportion = 0.42

n = sample size = 20

Plugging in the values, we get:

z = (0.75 - 0.42) / sqrt[(0.42 * 0.58) / 20]

z = 2.11

Therefore, the test statistic is 2.11.