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23 October, 13:58

When 480 college students were surveyed, 160 said they own a car. Construct a 95% confidence interval for the proportion of college students who say they own a car.

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  1. 23 October, 14:18
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    (0.291, 0.376)

    Step-by-step explanation:

    Confidence interval = mean or proportion ± margin of error

    CI = μ or p ± ME

    The proportion is p = 160/480 = 0.333.

    Margin of error = critical value * standard error

    For 95% confidence, CV = 1.960 (from t table).

    Standard error for a proportion is √ (pq / n), where n is the sample size, p is the proportion, and q is 1-p.

    Solving for margin of error:

    ME = 1.960 √ (0.333 * 0.667 / 480)

    ME = 0.042

    The confidence interval is:

    CI = 0.333 ± 0.042

    (0.291, 0.376)
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