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15 September, 07:32

In a 3M Privacy Filters poll, 806 adults were asked to identify their favorite seat when they fly, and 492 of them chose a window seat. Use a. 01 significance level to test the claim that the majority of adults prefer a window seat when they fly.

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  1. 15 September, 11:26
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    Step-by-step explanation:

    If majority of adults prefer a window seat when they fly, it means that more than half or more than 0.5 of the population prefer a window seat when they fly.

    We would set up the hypothesis test.

    For the null hypothesis,

    p = 0.45

    For the alternative hypothesis,

    p > 0.5

    Considering the population proportion, probability of success, p = 0.5

    q = probability of failure = 1 - p

    q = 1 - 0.5 = 0.5

    Considering the sample,

    Sample proportion, P = x/n

    Where

    x = number of success = 492

    n = number of samples = 806

    P = 492/806 = 0.61

    We would determine the test statistic which is the z score

    z = (P - p) / √pq/n

    z = (0.61 - 0.5) / √ (0.5 * 0.5) / 806 = 6.24

    From the normal distribution table, the p value < 0.00001

    Since alpha, 0.01 < than the p value, then we would reject the null hypothesis. Therefore, at a 1% significance level, we can conclude that the majority of adults prefer a window seat when they fly.
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