An article claims that teenagers on average will check their cellphones 150 times in one day. A student decides to test this claim using the hypotheses H0: μ = 150 vs. Ha: μ ≠ 150. A 95% confidence interval for the true mean is found to be (154.3, 167.5). On the basis of this interval, what should the student conclude at α=0.05?

Question

Bentley Clements

Mathematics

10 September, 00:43

An article claims that teenagers on average will check their cellphones 150 times in one day. A student decides to test this claim using the hypotheses H0: μ = 150 vs. Ha: μ ≠ 150. A 95% confidence interval for the true mean is found to be (154.3, 167.5). On the basis of this interval, what should the student conclude at α=0.05?

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Kevin Ritter · Answer 1

Answer with explanation:

The given set of hypothesis:

H0: μ = 150 vs. Ha: μ ≠ 150.

A 95% confidence interval for the true mean is found to be (154.3, 167.5).

[A 95% confidence interval interprets that a person can be 95% confident that the true population mean lies in it.]

But μ = 150 does not lie in the above interval (154.3, 167.5).

It means the null hypothesis gets rejected at α=0.05.

Thus, The student should conclude they have sufficient evidence to rejecte the article's claim that teenagers on average will check their cellphones 150 times in one day at α=0.05 (Significance).