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Question

Use a significance level of $0.05$ for all tests below.Research the percentages of each blood type that the Red Cross states are in the population. Now use your class as a sample. For each student note the blood type. Is the distribution of blood types in your class as expected based on the Red Cross percentages?

Solution

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Perform the chi-square goodness-of-fit test.

Determine the observed frequencies $O$.

The expected frequencies $E$ are the product of the sample size $n=40$ and the probabilities $\dfrac{1}{c}$ (with $c$ the number of categories).

The chi-square subtotals are the squared differences between the observed and expected frequencies, divided by the expected frequency.

$\chi^2_{sub}=\dfrac{(O-E)^2}{E}$

The value of the test-statistic is then the sum of the chi-square subtotals:

$\chi^2=\sum \dfrac{(O-E)^2}{E}$

Determine the critical value using table G with $df=c-1$ and $\alpha=0.05$.

If the test statistic $\chi^2$ is more than the critical value, then reject the null hypothesis.

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