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28 December, 15:57

g According to a New York Times/CBS News poll conducted during June 24-28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of 1810 American adults, 62% said that owning a home is a very important part of the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a 2% significance level, and use both the p-value and the critical-value approaches.

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  1. 28 December, 17:27
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    Step-by-step explanation:

    We would set up the hypothesis test.

    a) For the null hypothesis,

    P = 0.55

    For the alternative hypothesis,

    P > 0.55

    Considering the population proportion, probability of success, p = 0.55

    q = probability of failure = 1 - p

    q = 1 - 0.55 = 0.45

    Considering the sample,

    Probability of success, P = 0.62

    Number of samples, n = 1810

    We would determine the test statistic which is the z score

    z = (P - p) / √pq/n

    z = (0.62 - 0.55) / √ (0.55 * 0.45) / 1810 = 5.98

    Since this is a right tailed test, the critical value would be the p value to the right of z = 5.98

    p value = 0.00001

    Since alpha, 0.02 > than the p value, 0.00001, then we would reject the null hypothesis.

    Using the critical value approach, By using the critical region method,

    the calculated test statistic is 5.98 for the right tail and - 5.98 for the left tail

    Since α = 0.02, the critical value is determined from the normal distribution table.

    For the left, α/2 = 0.02/2 = 0.01

    The z score for an area to the left of 0.01 is - 2.325

    For the right, α/2 = 1 - 0.01 = 0.99

    The z score for an area to the right of 0.995 is 2.325

    In order to reject the null hypothesis, the test statistic must be smaller than - 2.325 or greater than 2.325

    Since - 5.98 2.325, we would reject the null hypothesis.

    Therefore, it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%.
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