Are the assumptions and the conditions to perform a one-proportion z-test met? O

Question

Are the assumptions and the conditions to perform a one-proportion z-test met? O No O Yes State the null and alternative hypotheses. Choose the correct answer below Ho:p=0.022 HA p 0.022 C. Ho:p= 0.022 HA p #0.022 D. The assumptions and conditions are not met, so the test cannot proceed Determine the z-test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A, z = (Round to two decimal places as needed ) O B. The assumptions and conditions are not met, so the test cannot proceed. Find the P-value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice d A. P-value- (Round to three decimal places as needed.) O B. The assumptions and conditions are not met, so the test cannot proceed What is your conclusion? Choose the correct answer below 0 A. Fail to reject Ho The proportion of twin births for teenage mothers is not different from the proportion of twin births for all mothers B. Reject Ho The proportion of twin births for teenage mothers is greater than the proportion of twin births for all mothers O C. Reject Ho . The proportion of twin births for teenage mothers is different from the proportion of twin births for all mothers 0 D. The assumptions and conditions are not met, so the test cannot proceed

Explanation / Answer

Solution:-

Yes, condisions are met.

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

Null hypothesis: P = 0.022
Alternative hypothesis: P 0.022

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it 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 ] = sqrt [(0.022 * 0.978) / 551] = 0.99986
z = (p - P) / = (0.018 - 0.022)/0.99986 = -0.004

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 two-tailed test, the P-value is the probability that the z-score is less than -0.004 or greater than 0.004.

We use the Normal Distribution Calculator to find P(z < -0.004), and P(z > 0.004)

The P-Value is 0.996808.
The result is not significant at p < 0.05.

Interpret results. Since the P-value (0.99) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Conclusion. Fail to reject null hypothesis. The proportion is same.

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