Approximately 13.2% of US drivers are younger than age 25, with 37.7% in the 25-44 age group, and 49.1% in the 45-and-over-category. For a r

Question

Approximately 13.2% of US drivers are younger than age 25, with 37.7% in the 25-44 age group, and 49.1% in the 45-and-over-category. For a random sample of 200 fatal accidents in her state, a safety expert finds that 42 drivers were under 25 years old, 80 were 25-44 years old, and 78 were at least 45 years old. At the 0.05 level, test whether the age distribution of drivers involved in fatal accidents within the state could be the same as the age distribution of all US drivers.

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Madeline 1 week 2021-11-25T05:51:58+00:00 1 Answer 0

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    2021-11-25T05:53:08+00:00

    Answer:

    could not be the same

    Step-by-step explanation:

    Given that approximately US drivers are agewise as follows:

    <25   13.2

    25-45   37.7%

    >45   49.1%

    Observations are made for a sample of 200 fatal accidents.

    Let us create hypotheses as

    H_0:  Proportions age wise are the same as for US drivers\\H_a: Proportions are different

    (Two tailed chi square test at 5% significance level)

    Age <25 25-45 >45  

    Expected 13.2 37.7 49.1 100

    Observed 42 80 78 200

    Expected no  26.4 75.4 98.2 200

    Chi square 9.218181818 0.280636605 4.155193483 13.65401191

    df = 2

    p value = 0.001084

    Since p <0.05 we reject null hypothesis

    At the  0.05 level, the age distribution of drivers involved in fatal accidents within the state could not be the same as the age distribution of all US drivers as there seems to be significant difference.

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