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positive critical value of a test

A random sample of 145 recent donations at a certain blood bank reveals that 74 were type A blood. Does this suggest that the actual percentage of type A donors differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01.

Let p represent the true proportion of donors that are type A. Identify the appropriate hypotheses for testing in this situation.
A. H0: p < 0.40 versus Ha: p = 0.40
B. H0: p = 0.40 versus Ha: p < 0.40
C. H0: p = 0.40 versus Ha: p > 0.40
D. H0: p > 0.40 versus Ha: p = 0.40
E. H0: p = 0.40 versus Ha: p 0.40

What is the positive critical value for this test?
Give answer to three decimal places.

What is the sample proportion ?
Give answer to three decimal places.

What is the test statistic of this test?
Give answer to three decimal places

With = 0.01, what do you conclude about the true proportion of donors with type A blood?
A. The true proportion of donors with type A blood is 0.510.
B. The true proportion of donors with type A blood is not 0.40 because the test statistic is in the rejection region.
C. This sample provides insufficient evidence, at the = 0.01 level, that the true proportion of people with type A blood is not 0.40.
D. The true proportion of donors with type A blood is 0.40 because the test statistic is in the rejection region.

Solution Preview

Let p represent the true proportion of donors that are type A. Identify the appropriate hypotheses for testing in this situation.
A. H0: p < 0.40 versus Ha: p = 0.40
B. H0: p = 0.40 versus Ha: p < 0.40
C. H0: p = 0.40 versus Ha: p > 0.40
D. H0: p > 0.40 versus Ha: p = 0.40
E. H0: p = 0.40 versus Ha: p 0.40

The answer is E. H0: p = 0.40 versus Ha: p is NOT ...

Solution Summary

The solution examines the positive critical value for this test.

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