Suppose a 95% confidence interval for the proportion of Canadians who exercise regularly is [0.30;0.42]. Which one of the following statements is FALSE? (a) We are at least 95% confident that more than 25% of Canadians exercise regularly. (b) We are at least 95% confident that more than 45% of Canadians exercise regularly. (c) The hypothesis that 33% of Canadians exercise regularly cannot be rejected at significance level α = 0.05 . (d) We are at least 95% confident that fewer than half of Canadians exercise regularly. (e) Several statements are false.

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19-12-2022
Mathematics

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Suppose a 95% confidence interval for the proportion of Canadians who exercise regularly is [0.30;0.42]. Which one of the following statements is FALSE? (a) We are at least 95% confident that more than 25% of Canadians exercise regularly. (b) We are at least 95% confident that more than 45% of Canadians exercise regularly. (c) The hypothesis that 33% of Canadians exercise regularly cannot be rejected at significance level α = 0.05 . (d) We are at least 95% confident that fewer than half of Canadians exercise regularly. (e) Several statements are false.

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debjitbhowal4568 debjitbhowal4568 · Answer 1 · 2022-12-25T22:16:42-05:00

The correct answer is (c): "The hypothesis that 33% of Canadians exercise regularly cannot be rejected at significance level α = 0.05".

The confidence interval [0.30;0.42] represents our estimate of the true proportion of Canadians who exercise regularly, with a confidence level of 95%. This means that if we were to repeat the survey multiple times, using the same sampling method and sample size, we would expect the confidence interval to contain the true proportion of Canadians who exercise regularly 95% of the time.

Based on the confidence interval provided, we can say that we are at least 95% confident that more than 30% and fewer than 42% of Canadians exercise regularly. This means that statements (a) and (d) are both true. However, statement (c) is false because the hypothesis that 33% of Canadians exercise regularly is not contained within the confidence interval, and therefore cannot be rejected at significance level α = 0.05.

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