uiz: WAQ #8 Chapter 8 Time Remaining: 03:5308 Submit Qu This Question: 1 pt 4 of
ID: 3350204 • Letter: U
Question
uiz: WAQ #8 Chapter 8 Time Remaining: 03:5308 Submit Qu This Question: 1 pt 4 of7 (5 This Quiz: 7 pts possib In a recent poll of 745 randomly selected adufts, 589 said that it is morally wrong to not report all income on tax retuns. Use a 0.05 signilicance level to test the claim that 70% of ad its say that it s morally wrong to not report all income on tax returns. Identify the nul hypothesis, alternative hypothesis, test statistic P value. n about the mull hypothesis, and final conclusion that addresses the origin al claim. Use the P-value method. Use the normal distribution as an approximation Idenüfy the correct null and aiternative hypotheses. Choose the correct answer below. A. Ho'p:0.7 O B. Ho: p 0.3 H,: p, 0.3 O D. Ho p 0.7 H,: p0.3 ok The test statistic is z(Round to two decimal places as needed.) nch Contents lor The P-value is(Round to four decimal places as needed ) Identty the conclusion about the null hvoothesis and the final conclusion that addresses the see scona ozExplanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.70
Alternative hypothesis: P 0.70
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 ]
= 0.01679
z = (p - P) /
z = 5.396
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 - 5.396 or greater than 5.396.
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 have to reject the null hypothesis.
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