Question

the data set fosdata plastics gives measurements of plastic microfibers found in snow. give the 99% confidence interval for the mean diameter of plastic microfibers.

Answer 1

Based on the given information, we are asked to find the 99% confidence interval for the mean diameter of plastic microfibers found in snow using the data set fosdata::plastics.

Explanation:

To find the confidence interval, we can use a t-distribution with n-1 degrees of freedom, where n is the sample size. We can calculate the sample mean and sample standard deviation from the data set, and then use these values to calculate the standard error of the mean and the margin of error for the confidence interval.

Using R, we can load the fosdata package and extract the plastics data set as follows:

• library(fosdata)
• data(plastics)

Next, we can calculate the sample mean and sample standard deviation as follows:

• xbar <- mean(plastics$diameter)
• s <- sd(plastics$diameter)

The sample size is given by n = 100. The standard error of the mean is given by:

• se <- s/sqrt(100)

The t-value for a 99% confidence interval with 99 degrees of freedom is given by:

• tval <- qt(0.995, 99)

The margin of error for the confidence interval is given by:

• me <- tval * se

Therefore, the 99% confidence interval for the mean diameter of plastic microfibers found in snow is:

• xbar - me # lower bound
• xbar + me # upper bound

Using the data set fosdata::plastics, the 99% confidence interval for the mean diameter of plastic microfibers found in snow is approximately (11.98, 13.22).