What is the test statistic? z=____ (Round to two decimal places as needed.) What

Question

What is the test statistic?

z=____

(Round to two decimal places as needed.)

What is the P-value?

P-value=_____

(Round to four decimal places as needed.)

Score: 0.2 of 1 pt 13 of 35 (18 complete) Hw Score: 44.36%, 15.53 of 35 pts 8.3.14-T Question Help A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this writing, 277 babies were born to parents using the new method, and 243 of them were boys. Usea 0.05 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 Which of the following is the hypothesis test to be conducted? 0 A. Ho : p=0.5 B. Ho:p#0.5 H1 p 0.5 Ho:p>o.5 H1 :p=0.5 Ho: p = 0.5 H1 : p #0.5 Hy p 0.5 C. Ho:p=0.5 H1 p>0.5 0 E. Hops 0.5 H1 : p= 0.5 O D. F. What is the test statistic? (Round to two decimal places as needed.)

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.01972
z = (p - P) /

z = 19.13

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 19.13.

Thus, the P-value = less than 0.0001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we cannot accept the null hypothesis.

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