College

A student reads that a recent poll finds that a 95% confidence interval for the mean ideal weight given by adult American women is 139 (plus or minus) 1.4 pounds.

Asked to explain the meaning of this interval, the student says, "95% of all adult American women would say that their ideal weight is between 137.6 and 140.4 pounds."

Is the student right? Explain your answer.

Answer :

Answer:

Yes, the student is right

Step-by-step explanation:

95% confidence interval for the mean ideal weight given by adult American women is 139 (+ or -) 1.4 pounds

Mean = 139 pounds

Error margin = 1.4 pounds

Lower limit = 139 - 1.4 = 137.6

Upper limit = 139 + 1.4 = 140.4

The ideal weight is between 137.6 and 140.4 pounds

Final answer:

The student is not right. The 95% confidence interval for the mean ideal weight given by adult American women is 139 ± 1.4 pounds. It does not mean that 95% of all adult American women would say that their ideal weight is between 137.6 and 140.4 pounds.

Explanation:

The student is not right. The 95% confidence interval for the mean ideal weight given by adult American women is 139 ± 1.4 pounds. This means that we can be 95% confident that the true mean ideal weight for all adult American women falls within the range 137.6 to 140.4 pounds. It does not mean that 95% of all adult American women would say that their ideal weight is between 137.6 and 140.4 pounds. The confidence interval provides information about the precision and reliability of the estimated mean, not individual responses.

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