Answer:
a. A point estimate of the BMI for adults in the United States can be calculated from the sample mean, which has a value M=44.57.
b. The sample standard deviation is s=79.9507.
c. The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).
Step-by-step explanation:
We start by calculating the sample mean and standard deviation of the BMI data:
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=44.57.
The sample size is N=75.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The degrees of freedom for this sample size are:
The t-value for a 95% confidence interval and 74 degrees of freedom is t=1.993.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the BMI of adults in the United States is (26.18, 62.96).