ment FULL SCREEN PRINTER VERSION BACK NEXT of children under the age of 18 years
ID: 3234074 • Letter: M
Question
ment FULL SCREEN PRINTER VERSION BACK NEXT of children under the age of 18 years in the United States lived with two parents in 2009, suppose that in a recent sample According to the U.S. Census Bureau, 6S% of 1975 children, 1243 were living with two parents. 0.1 test whether the current percentage of all children under the age of 18 years in the United States who live with two a. Using the critical value approach and parents is different from 69% Enter the critical values in increasing order. Round your answer for Z to two decimal places. observed Z critical value Critical value the null hypothesis. We 69% 18 years in the United States who live with two parents is We conclude that the current percentage of all children under the age ofExplanation / Answer
Solution:-
x = 1243, n = 1975
p = 1243/1975
p = 0.6294
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.69
Alternative hypothesis: P 0.69
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 0.10. 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 ]
= 0.01087
z = (p - P) /
z = - 5.57
zcritical = + 1.645
rejection region is - 1.645 > z > 1.645
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 z test statistic(5.57) lies in the critical region hence we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that population proportion is not equal to 0.69.
b) The Type I error occur when we conclude that the current percentage of all children under the age of 18 years in the united states who live with two parents is not equal to 69%, when it is actully equal to 69%.
P(Type I error) = 0.10
c)
Since we have a two-tailed test, the P-value is the probability that the z-score is less than - 5.57 or greater than 5.57.
Thus, the P-value = Less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.02), we have to reject the null hypothesis.
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