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body mass index and AP opinion polls

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1) A student reads that a 95% confidence interval for the mean body mass index (BMI) of young American women is 26.8 ± 0.6. Asked to explain the meaning of this interval, the student says, "95% of all young women have BMI between 26.3 and 27.4." Is this explanation correct? Explain your answer.

2) You ask another student to explain the confidence interval for mean BMI described in the previous exercise. The student answers, "We can be 95% confident that future samples of young women will have mean BMI between 26.2 and 27.4." Is this explanation correct? Explain your answer.

3) Here is an explanation from the Associated Press concerning one of its opinion polls. Explain briefly but clearly in what ways this explanation is incorrect:

For a poll of 1,600 adults, the variation due to sampling error is no more than three percentage points either way. The error margin is said to be valid at the 95% confidence level.

This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within three percentage points of the results of this survey.

4) When asked to explain the meaning of the "P-value was P = 0.03," a student says, "This means there is only probability 0.03 that the null hypothesis is true." Explain what P = 0.03 really means in a way that makes it clear that the student's explanation is wrong.

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