a. 68% of the sample believed global warming is caused by human activities.
b. The hypothesis test did not reject the idea that the percentage changed from 57%.
c. i. In 2017, the percentage is not significantly different from 57%.
c. ii. In 2017, the percentage of Americans who believe global warming is caused by human activities has changed from the historical level of 57%.
In March 2017, a Gallup poll comprising a random sample of 1018 Americans revealed that 692 individuals believed global warming is caused by human activities. To ascertain the proportion of the sample subscribing to this view, the calculation is as follows:
a. The percentage of the sample believing that global warming is caused by human activities is \( \frac{692}{1018} \times 100 \approx 67.94\%.
b. To assess whether the proportion has deviated from the historical figure of 57%, a hypothesis test is conducted. Employing a significance level of 0.01%, the null hypothesis posits no change, while the alternative hypothesis contends a significant alteration.
c.(i). The correct interpretation is determined through the p-value. If the p-value is greater than 0.01, the null hypothesis is retained, suggesting that, in 2017, the percentage of Americans affirming human-induced global warming is not significantly different from the historical 57% .
(ii). Conversely, if the p-value is less than 0.01, the null hypothesis is rejected, implying that, in 2017, the percentage has indeed shifted from the historical level of 57%.