Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. Compute the test statistic.Group of answer choices21.201.541.35
Question
Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president. Compute the test statistic.Group of answer choices21.201.541.35
Solution
To compute the test statistic, we need to use the formula for the test statistic in a two-proportion z-test. The formula is:
z = (p1 - p2) / sqrt [ (p(1 - p)) * ( (1/n1) + (1/n2) ) ]
where:
- p1 is the proportion of success in the first group,
- p2 is the proportion of success in the second group,
- p is the pooled proportion,
- n1 is the size of the first group,
- n2 is the size of the second group.
First, we need to calculate the proportions:
- p1 = 120 / 300 = 0.4 (proportion of females planning to vote for the incumbent president)
- p2 = 140 / 400 = 0.35 (proportion of males planning to vote for the incumbent president)
Next, we calculate the pooled proportion:
- p = (120 + 140) / (300 + 400) = 260 / 700 = 0.3714
Now we can substitute these values into the formula:
z = (0.4 - 0.35) / sqrt [ (0.3714 * (1 - 0.3714)) * ( (1/300) + (1/400) ) ]
After performing the calculations, we get:
z = 0.05 / sqrt [ (0.3714 * 0.6286) * (0.00333 + 0.0025) ]
z = 0.05 / sqrt [ 0.2334 * 0.00583 ]
z = 0.05 / sqrt [ 0.00136 ]
z = 0.05 / 0.0369
z = 1.35
So, the test statistic is 1.35.
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