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Testing Proportions

A survey dating back to the 1990's suggested that Americans anticipated a reduction in living standards and that a steadily increasing consumption no longer might be as important as it was in the past. (Were they right?)

Suppose that a poll of 2000 people indicated 1373 in favor of forcing a reduction in the size of American automobiles by legislative means.

Would you expect to observe as many as 1373 in favor of this proposition if, in fact, the general public was split 50-50 on the issue?

Justify your answer.

Solution Preview

For this problem, we can use a one-sided, one-sample z-test to determine if the observed proportion in favor of forcing a reduction in the size of American automobiles by legislative means (1373/2000 = 0.6865) is significantly greater than the assumed proportion of 0.50.

[It is a z-test because it involves proportions (as opposed to means, for which we would use a z-test or a t-test, depending on the situation). It is one-sided because we are testing that the sample proportion is above a given number as opposed to not-equal to it. It is one-sample because we are comparing the sample proportion to a given number instead of to another sample proportion.]

The null ...

Solution Summary

The solution uses a z-test of proportions to answer the question "Would you expect to observe as many as 1373 in favor of this proposition?".

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