Usher / Hw10 Secure https://webwork.uoregon.edu/webwork2/Math243Fall Duckweb re
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Usher / Hw10 Secure https://webwork.uoregon.edu/webwork2/Math243Fall Duckweb re Blackboard University of Orego . YouTube .. NASTY GAL /meffectieuserststimsozauser=tsumoza ya5bdgn GoDucks.comNews Popular D U of O UNICEF Cam. HW10: Problem 7 blem 7 tings PreviousProblem List Next (1 point) An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n = 76 C of l students found 28 with brown eyes. We test blems Ho:p=.45 Ha : p.45 (a) What is the z-statistic for this test? 3 (b) What is the P-value of the test? Note: You can earn partial credit on this problem. Preview My AnswersSubmit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor Page generated at 12/01/2017 at 0225pm PSTExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.45
Alternative hypothesis: P 0.45
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 ]
= 0.0571
z = (p - P) /
z = - 1.43
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 -1.43 or greater than 1.43.
Thus, the P-value = 0.1528
Interpret results. Since the P-value (0.1528) is greater than the significance level (0.05), we cannot reject the null hypothesis.
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