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08.03)Esther wants to know if the number of words on a page in her language arts book is generally more than the number of words on a page in her social studies book. She takes a random sample of 25 pages in each book and then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.

Book Mean Median Mean Absolute Deviation
Language arts 78.5 60 14.2
Social studies 68.7 65 9.8

She claims that because the mean number of words on each page of the language arts book is greater than the mean number of words on each page of the social studies book, the language arts book has more words per page. Based on the data, is this a valid inference?

  • math -

    I assume that "absolution deviation" means the same as standard deviation (SD).

    Z = (score-mean)/SD

    Z = (mean1 - mean2)/standard error (SE) of difference between means

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√n

    If only one SD is provided, you can use just that to determine SEdiff.

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability
    related to the Z score to compare with the level of significance you are using.

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