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3. The following table lists the frequency distribution for 60 rolls of a die.

Outcome 1-spot 2-spot 3-spot 4-spot 5-spot 6-spot
Frequency 7 12 8 15 11 7

Using the “Goodness of Fit” test at the 5% level of significance, test whether the null hypothesis that the given die is fair is true. (Hint: If the die is fair, each “spot” has the same chance of appearing). Use the back of the page for work if needed.

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  1. Use the Chi-square (X^2) method.

    X^2 = ∑ (O-E)^2/E, where O = observed frequency and E = expected frequency.

    ∑ = sum of all the cells.

    E = (column total * row total)/grand total

    df = n - 1, where n = number of cells

    Look up value in X^2 table in the back of your textbook.

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