Hypothesis Test In a survey of 1,010 randomly selected American adults, 28% resp
ID: 3234755 • Letter: H
Question
Hypothesis Test In a survey of 1,010 randomly selected American adults, 28% responded that they thought the best chance to obtain more than $500,000 in their lifetimes was to win a lottery or sweepstakes. Does this provide convincing evidence that more than one fourth of US adults see a lottery or sweepstakes win as their best chance of accumulating $500,000? Carry out a test using a significance level of .01.
State the original claim symbolically using appropriate notation.
State H0 symbolically using appropriate notation.
State H1 symbolically, using appropriate notation, and state clearly why you have a left tailed, right tailed, or two tailed test.
Show how you use the appropriate calculators to compute the test statistic and the P value.
Explain clearly whether your results have you rejecting or failing to reject the null hypothesis, and state clearly why your make that decision.
Based on your decision about H0, make a clear statement about what you can now say about the original claim. Make sure you write a clear contextual sentence that includes the original claim.
Explanation / Answer
Solution:-
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P <= 0.25, i.e.,less than or equal to one fourth of US adults see a lottery or sweepstakes win as their best chance of accumulating $500,000
Alternative hypothesis: P > 0.25, i.e.,more than one fourth of US adults see a lottery or sweepstakes win as their best chance of accumulating $500,000
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too large.
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 ] = sqrt [(0.25 * 0.75) / 1010] = 0.0136251078659
z = (p - P) / = (0.28 - 0.25)/0.0136251078659 = 2.20181743112 or 2.202
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 one-tailed test, the P-value is the probability that the z-score is less than 2.202. We use the Normal Distribution Calculator to find P(z < 2.202)
The P-Value is 0.013833.
Interpret results. Since the P-value (0.013833) is slightly more than the significance level (0.01), we can accept the null hypothesis.Thus we are failing to reject null hypothesis.
Conclusion. We did not find sufficient evidence to claim that more than one fourth of US adults see a lottery or sweepstakes win as their best chance of accumulating $500,000
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