Most Common Automobile Color
Help finding test statistic?
We think that the most common color for automobiles is silver and that 24% of all automobiles sold are silver. We take a random sample of 225 cars an find that 63 of them are silver. Calculate the test-statistic for this data.
The answer is 1.40
WHY?
Since we’re dealing with a sample set (not the full population), I was taught to call it z-statistic. Anyways, I get 1.404879 using this:
z = (observed – expected) / s.e.
s.e. = sample standard error = sqrt(observed ratio*(1-expected ratio) / n)
where n = sample size
The expected ratio is 24%, but the sample observed 28% (=63/225).
s.e. = sqrt (.28*(1-.24)/225) = 0.028472209
so then, z = (.28-.24) / 0.028472209 = 1.404879
This seemed to come up with your given answer. Try it with some others to confirm these formulas.
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