Question

FiftyFifty adult men in the United States are randomly selected and measured for their body mass index​ (BMI). Based on that​ sample, it is estimated that the average​ (mean) BMI for men is 26.526.5​, with a margin of error of 3.23.2. Use the given statistic and margin of error to identify the range of values​ (confidence interval) likely to contain the true value of the population parameter.

Answer 1

(23.3, 29.7)

Explanation:

We are given the following information the question:

Sample mean = 26.5

Sample size = 50

Margin of error = 3.2

Confidence Interval:

`\text{Sample mean} \pm \text{Margin of error}\\= 26.5 \pm 3.2 = (23.3, 29.7)`

Thus, the true value of the population parameter lies in the range (23.3, 29.7)

Answer 2

Answer:
`(23.3,\ 29.7)`

Explanation:

The confidence interval for population mean is given by :-

`\overline{x}\pm ME.`, where
`\overline{x}` is the sample mean and ME is the margin of error .

Given : The sample mean :
`\overline{x}=26.5`

Margin of error :
`ME=3.2`

Then , the range of values​ (confidence interval) likely to contain the true value of the population parameter will be :-

`26.5\pm 3.2=(26.5-3.2,\ 26.5+3.2)=(23.3,\ 29.7)`

Hence, the range of values​ likely to contain the true value of the population parameter =
`(23.3,\ 29.7)`