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A newspaper poll asked respondents if they trusted "eco friendly" labels on cleaning products. Out of 1000 adults surveyed, 498 responded "yes." We would like to test if the proportion of respondents that trust these labels is at least 50%.
-At the 0.01 level of significance, the correct conclusion is
A) do not reject the alternative hypothesis.
B) reject the null hypothesis.
C) there is no evidence that at least 50% of respondents trust "eco-friendly" labels.
D) fail to reject the null hypothesis. There is no evidence that the proportion of respondents that trust "eco-friendly" labels is less than 50%.
E) reject the null hypothesis. There is strong evidence that the proportion of respondents that trust "eco-friendly" labels is less than 50%.

Question

Quizplus · Accepted Answer

The null hypothesis in this scenario is that the proportion of respondents who trust "eco-friendly" labels is at least 50% (p ≥ 0.5). With 498 out of 1000 respondents saying "yes," the sample proportion is 0.498, which is very close to 0.5. At a 0.01 level of significance, the difference is not statistically significant enough to reject the null hypothesis. Therefore, we fail to reject the null hypothesis, indicating there is no evidence that the proportion trusting "eco-friendly" labels is less than 50%.

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