est: Test #2 Chapters 6 through 9 Submit Tes his Question: 1 pt 13 of 20 (10 com
ID: 3350729 • Letter: E
Question
est: Test #2 Chapters 6 through 9 Submit Tes his Question: 1 pt 13 of 20 (10 complete) This Test: 20 pts possib In a recent poll of 755 randomly selected adults, 589 said that it is morally wrong to not report all income on tax retuns. Use a 0,01 significance level to test the claim that 70% of adults say that it is morally wrong to not report al income on tax returns. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conckusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P.value method Use the normal distribution as ana identify the correct null and alternative hypotheses. Choose the correct answer below. O A. Hop 0.3 O B. Ho: p 0.3 H,: pt 0.3 O D. Ho: p-0.7 H,, p#0.7 H p>0.3 C. Ho' p=0.3 H: p0.7 ok The test statistic isz(Round to two decimal places as needed) nch The P-value is (Round to four decimal places as needed) idenilit the conclusion about the null hwoothesis and the final conclusion that addresses the oriinal claim urchaseExplanation / 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 0.01. 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 ]
= 0.0166777
z = (p - P) /
z = 4.80
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 - 4.80 or greater than 4.80.
Thus, the P-value = less than 0.001
Interpret results. Since the P-value (less than 0.001) is less than the significance level (0.01), we have to reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that 70% adults says that it is morally wrong to not report all income on tax returns.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.