In a recent year, a poll asked 2295 random adult citizens of a large country how

Question

In a recent year, a poll asked 2295 random adult citizens of a large country how they rated economic conditions. In the poll, 17% rated the economy as Excellent/Good. A recent media outlet claimed that the percentage of citizens who felt the economy was in Excellent/Good shape was 14%. Does the poll support this claim? a) Test the appropriate hypothesis. Find a 99% confidence interval for the proportion of adults who rated the economy as Excellent/Good. Check conditions. b) Does your confidence interval provide evidence to support the claim? c) What is the significance level of the test in b? Explain. a) Let p be the proportion of adult citizens who felt the economy was in Excellent/Good shape. What are the null and alternative hypotheses for the test? A. H_0: p = 0.14 vs. H_A: p > 0.14 B. H_0: p = 0.14 vs. H_A: p notequalto 0.14 C. H_0: p = 0.17 vs. H_A: p notequalto 0.17 D. H_0: p = 0.17 vs. H_A: p

Explanation / Answer

a) Null and alternative hypotheses: Option B is correct.

The statistical software output for 99% confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

Hence,

99% confidence interval will be:

(0.15, 0.19)

b) No, the confidence interval doesn't contain 0.14 and hence, it doesn't support the claim.

c) Significance level = 0.01

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 390.15 2295 0.17 0.0078410128 0.14980289 0.19019711

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