Question

a politician claims that 55 ​% of voters in a certain area have voted for an independent candidate in past elections. Suppose you surveyed 25 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 ​55 %. What value of the test statistic should you​ report? The test statistic is z=

Answer 1

To calculate the test statistic (z-score) for this hypothesis test you can use the formula:

z = (p - P) / √((P * (1 - P)) / n)

Where:

p is the sample proportion (proportion of people in the sample who voted for an independent candidateP is the hypothesized population proportion (55%n is the sample size (25).

In this case p = 15/25 = 0.60 P = 0.55 and n = 25.

Now substitute these values into the formula:

z = (0.60 - 0.55) / √((0.55 * (1 - 0.55)) / 25)

Simplifyingz = (0.05) / √((0.55 * 0.45) / 25)

z = (0.05) / √(0.13475)

z ≈ 0.05 / 0.3672

z ≈ 0.1361

Therefore the test statistic (z-score) is approximately 0.1361.