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

Answer: $(23.3,\ 29.7)$

Step-by-step 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 =  $(23.3,\ 29.7)$

Answer 2

Answer:

(23.3, 29.7)

Step-by-step 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)