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31 December, 17:04

The head circumference is measured for 25 girls and their younger twin sisters. The mean of the older twin girls was 50.23 cm and the mean of the younger twins was 49.96 cm. The standard deviation of the differences was 1 cm. Is this difference significant at a significance level of 5% (i. e., α = 0.05) ?

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  1. 31 December, 18:06
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    Step-by-step explanation:

    The data for the test are the differences between the head circumferences of the older twin girls and that of their sisters

    μd = mean head circumferences of the older twin girls minus the mean head circumferences of the sisters

    For the null hypothesis

    H0: μd ≥ 0

    For the alternative hypothesis

    H1: μd < 0

    It is a left tailed test

    The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 25 - 1 = 24

    The formula for determining the test statistic is

    t = (xd - μd) / (sd/√n)

    Where

    xd = difference in sample means

    μd = difference in population means

    sd = standard deviation of the difference

    From the information given,

    xd = 50.23 - 49.96 = 0.27

    t = (0.27 - 0) / (1/√25)

    t = 1.35

    We would determine the probability value by using the t test calculator.

    p = 0.095

    Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.

    Therefore, at 5% significance level, the difference is not significant
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