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Question

Use a significance level of 0.050.05 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?

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

Determine the observed frequencies OO.

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

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

χsub2=(OE)2E\chi^2_{sub}=\dfrac{(O-E)^2}{E}

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

χ2=(OE)2E\chi^2=\sum \dfrac{(O-E)^2}{E}

Determine the critical value using table G with df=c1df=c-1 and α=0.05\alpha=0.05.

If the test statistic χ2\chi^2 is more than the critical value, then reject the null hypothesis.

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