Provide Explanation not just answers. Thanks Have a nice day You wish to test th
ID: 2931587 • Letter: P
Question
Provide Explanation not just answers. Thanks Have a nice day
You wish to test the following claim (Ha) at a significance level of = 0.005. H: Pi = P2 H : pl > P2 You obtain 315 successes in a sample of size n1-372 from the first population. You obtain 213 successes in a sample of size n2-267 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the z-score of the critical value? (Report answer accurate to three decimal places.) Question 4 Chap 10 What is the standardized test statistic for this sample? (Report answer accurate to three decimal places.) The test statistic is... Oin the critical region Onot in the critical region This test statistic leads to a decision to... O reject the null Oaccept the null O fail to reject the nullExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P1< P2
Alternative hypothesis: P1 > P2
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.005. The test method is a two-proportion z-test.
Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).
zcritical = 2.575
The null hypothesis would be rejected if z score is more than 2.575.
p = (p1 * n1 + p2 * n2) / (n1 + n2)
p = 0.8263
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
S.E = 0.0304
z = (p1 - p2) / SE
z = 1.613
where p1 is the sample proportion in sample 1, where p2 is the sample proportion in sample 2, n1 is the size of sample 1, and n2 is the size of sample 2.
Since we have a one-tailed test, the P-value is the probability that the z-score is more than 1.613.
Thus, the P-value = 0.0537
The test statistics does not lie in critical region.
Interpret results. Since the P-value (0.0537) is greater than the significance level (0.005), we cannot reject the null hypothesis.
Fail to reject the null hypothesis.
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