91Ó°ÊÓ

I. The average height of 48 male Swedes in the study was 71 inches.

$\stackrel{¯}{x}=71$inches

ii. The population of distinct ethnic groups has a 3 inch standard variance in height.

$\mathrm{σ}=3$inches

iii. The total number of male Swedes polled from various ethnic groups is, n=48

The random variables X and $\stackrel{¯}{X}$:

The average height of 48 Swiss guys is role="math" localid="1648640680776" $\stackrel{¯}{X}$, and the Swiss male's height is X.

The problem is solved with a normal distribution. For the population's standard deviation, we know that the sample size is greater than 30.

I. State the confidence interval. CI - (70.151,71,49)

ii. The graph is given below,

iii. The error bound is calculated from the formula,

EBM =$\frac{upperlimit-lowerlimit}{2}$

EBM = $\frac{71.849–70.151}{2}$

EBM = 0.849

The confidence interval will shrink in size as the sample size grows. As we know, when all parameters remain constant, increasing the sample size reduces variability.

As a result, we do not require a larger interval to capture the true population mean.