20 A clinical trial was conducted using a new method designe

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A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this writing, 285?

babies were born to parents using the new method, and 236 of them were boys. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a boy. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

HO: p   is > or, < or, = to or, not= to 0.5?_______

H1: p   is > or, < or, = to or, not= to 0.5?_______

b. What is the test statistic? z= _______

(Round the final answer to two decimal places as needed.)

c. What is the P-value?    P-value= ________

(Round to four decimal places as needed.)

d. What is the conclusion?

A. There is sufficient evidence to support the claim.

B. There is not sufficient evidence to support the claim

e. Is the conclusion valid today? Why or why not?

A.Yes, the conclusion is valid

B.No, the conclusion is not valid

C. You can make no decisions about the validity of the conclusion

Solution

HO: p = to 0.5

H1: p is > 0.5

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(b) The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(236/285-0.5)/sqrt(0.5*0.5/285)

=11.08

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(c) It is a right-tailed test.

So the p-value= P(Z>11.08) =0 (from standard normal table)

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(d)A. There is sufficient evidence to support the claim.

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(e)A.Yes, the conclusion is valid