A health study estimates the standard deviation of daily step counts as $\sigma =9.8$. How many participants are required to estimate the mean daily steps within $2$ steps with $99\%$ confidence?

A health study estimates the standard deviation of daily step counts as $s=9.8$. The minimum number of participants required to estimate the mean daily steps within $2$ steps, with $99\%$ confidence, is found to be $n=160$. What effect does doubling the required accuracy have on the sample size?

A researcher collects a simple random sample of size $n=12$ from a population that is normally distributed. The sample mean, $\bar{x}$, is $95$, and the sample standard deviation, $s$, is $8$. Construct a $98\%$ confidence interval for the population mean $\mu$. How does decreasing the sample size affect the margin of error, $E$?

Population $X$ has a standard deviation ${\sigma }_X=8$, and population $Y$ has a standard deviation ${\sigma }_Y=12$. How many times larger than Population $X$'s sample size does Population $Y$'s sample size need to be to achieve the same margin of error for the mean?

True or false: If samples of size $n=5$ are drawn from a highly skewed population with finite variance, the distribution of the sample mean, $\bar{X}$, is approximately normal.