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26 May, 20:39

It is claimed that 10 year old boys and girls both have the same average height (52 inches). A researcher studies 65 boys and finds that their average height is 52.8 with a variance of 98. The 111 girls in the study had an average height of 54.1 with a variance of 123. Construct a 95% confidence interval for the difference in the heights of 10 year old boys and girls based on these samples. Does the confidence interval support the claim that 10 year old boys and girls have the same average height?

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  1. 26 May, 20:45
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    Step-by-step explanation:

    Let us calculate std dev and std error of two samples

    Sample N Mean Std dev Std error

    1 65 52.8 9.9 1.22279

    2 111 54.1 11.09 1.0526

    Assuming equal variances

    df = 111+65-2=174

    Pooled std deviation = combined std deviation = 10.6677

    Pooled std error = 10.6677/sqrt 174 = 0.808

    difference in means = 52.8-54.1 = - 1.3

    Margin of error = 0.5923

    (t critical 1.6660)

    Confidence interval

    = (-4.4923, 1.8923)

    Since 0 lies in this interval we can accept null hypothesis that 10 year old boys and girls have the same average height
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