10. A physician claims that as soon as his patients have a positive pregnancy test, he is generally able to predict the sex of the baby and that his probability of being right is greater than the one-half that would be expected if he were just guessing. A skeptic challenges his claim, and the physician decides to collect data for the next ten pregnancies to try to support his claim.

(a) From the perspective of the physician, what are the null and alternative hypotheses for this situation?

H0: Probability (=,<,> or not equal to) ,___________ that the prediction is correct

Ha: Probability (=,<,> or not equal to) ,___________ that the prediction is correct.

(b) Out of the ten pregnancies, he is correct six times. Write in words what probability needs to be computed to find the p-value.

The necessary probability (the p-value) is the probability of 6 or more correct predictions in 10 tries if the long-run probability for a correct prediction is __________.

(c) The p-value for this test is .371. Does that prove that the skeptic is correct?

(yes or no).

(d) State the appropriate conclusion, using α = .05.

The null hypothesis (should be rejected or cannot be rejected)

(e) Assuming that the physician really does have some ability to make these predictions, what would you recommend that he do to increase the chance of proving his claim?

Make predictions for a (larger or smaller) sample of pregnancies.

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11. Explain which type of error, type 1 or type 2, could be made in each of the following cases.

(I) The null hypothesis is true.

A) It would happen if the null hypothesis is rejected

B) It would happen if the null hypothesis is true

C) It would happen if the null hypothesis is not rejected

D) It would happen if the alternative hypothesis is true

(II) The alternative hypothesis is true.

A) It would happen if the null hypothesis is rejected

B) It would happen if the null hypothesis is true

C) It would happen if the null hypothesis is not rejected

D) It would happen if the alternative hypothesis is true

(III) The null hypothesis is not rejected.

A) It would happen if the null hypothesis is rejected

B) It would happen if the null hypothesis is true

C) It would happen if the null hypothesis is not rejected

D) It would happen if the alternative hypothesis is true

(IV) The null hypothesis is rejected.

A) It would happen if the null hypothesis is rejected

B) It would happen if the null hypothesis is true

C) It would happen if the null hypothesis is not rejected

D) It would happen if the alternative hypothesis is true

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