The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological testdeveloped to measure the degree of Mexican/Spanish versu

Question

The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological testdeveloped to measure the degree of Mexican/Spanish versus Anglo/Englishacculturation of Mexican Americans. The distribution of ARSMA scores in a populationused to develop the test was approximately normal, with mean 3.0 and standarddeviation 0.8. A further study gave ARSMA to 50 first-generation Mexican Americans.The mean of their scores is x bar = 2.36. If the standard deviation for the first-generationpopulation is also 0.8.

Required:
Give a 95% confidence interval for the mean ARSMA score forfirst-generation Mexican Americans

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Tryphena 4 years 2021-08-17T23:33:20+00:00 1 Answers 35 views 0

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  1. Gerda
    0
    2021-08-17T23:34:53+00:00
    Reply

    Answer:

    95% confidence interval for the mean ARSMA score for first-generation Mexican Americans

    (2.13264 , 2.58736)

    Step-by-step explanation:

    Step(i):-

    Mean of the Population = 3.0

    Standard deviation of the Population = 0.8

    Given Mean of the sample(x⁻ ) = 2.36

    Standard deviation of the sample  (S) = 0.8

    size of the sample = 50

    Level of significance =0.05

    Degrees of freedom = n-1 = 50-1 = 49

    t_{\frac{0.05}{2} , 49} = 2.0096

    Step(ii):-

    95% confidence interval for the mean ARSMA score for first-generation Mexican Americans

    (x^{-} - t_{(\frac{\alpha }{2},df )} \frac{S}{\sqrt{n} } , (x^{-} +t_{(\frac{\alpha }{2},df )} \frac{S}{\sqrt{n} })

    (2.36 - 2.0096 \frac{0.8}{\sqrt{50} } , 2.36 +2.0096\frac{0.8}{\sqrt{50} })

    ( 2.36 – 0.22736 , 2.36 + 0.22736)

    (2.13264 , 2.58736)

    Final answer:-

    95% confidence interval for the mean ARSMA score for first-generation Mexican Americans

    (2.13264 , 2.58736)

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