Question

1. In June 2013, the Gallup organization had surveyed 1134 American adults and found that 360 had confidence in public schools. A year later, in June 2014, Gallup surveyed 1134 American adults and found that 298 had confidence in the public schools. A newspaper reporter saw the data and wrote the headline "Confidence in Schools Deteriorates.'" Test the hypothesis that the of proportion of Americans who have confidence in the public school systems is significantly less in 2014 than in 2013. a. What type of test will you use? b. Check Conditions: c. State Ho and H: d. State the p-value- e. Conclusion: oudonte learning a

Answer 1

(a) Here, we have to use two proportions z-test.

(b) Here, the sampling method for each population is simple random sampling and the samples are independent. Also, each sample includes at least 10 successes and 10 failures. Hence, the conditions have been met.

(c) Here, p1 = population proportion of American adults who had confidence in public schools in 2013 and p2 = population proportion of American adults who had confidence in public schools in 2014. Hence, H₀: p1 = p2 versus H₁: p1 > p2.

(e) Since p-value = 0.0021 < alpha = 0.05 (level of significance), we reject H0.
We conclude that there is enough evidence to suggest that the proportion of American adults who had confidence in public schools is significantly less in 2014 than in 2013.

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