As part of a Pew Research Center poll, subjects were asked if there is solid evi
ID: 3300069 • Letter: A
Question
As part of a Pew Research Center poll, subjects were asked if there is solid evidence that the earth is getting warmer. Among 1501 respondents, 20% said that there is not such evidence. Use a 0.01 significance level to test the claim that less than 25% of the population believes that there is not solid evidence that the earth is getting warmer. What is a possible consequence of a situation in which too many people incorrectly believe that there is not evidence of global warming during a time when global warming is occurring?Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P > 0.25
Alternative hypothesis: P < 0.25
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion 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 ]
= 0.0112
z = (p - P) /
z = - 4.46
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 - 4.46.
Thus, the P-value = less than 0.0001
Interpret results. Since the P-value (almost 0) is less than the significance level (0.01), we cannot accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that less than 25% of the population believes that there is not solid evidence that the earth is getting warmer.
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