Question

1. the bureau of labor statistics uses a complex sampling method to estimate the overall unemployment rate every month. the sampling method has low bias and low variability for estimating the unemployment rate.

a. what is meant by low bias?
b. what is meant by low variability?

1. for a recent season of major league baseball, miguel wants to estimate the average number of total runs scored per game. he plans to take an srs of 20 games and use the mean of the sample as the estimate.

the simulation results below display 10 sample means from 10 separate simple random samples of 20 games each.
7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 estimate of the mean number of runs
a. based on the dotplot, estimate the true mean number of runs scored per game. explain your reasoning.
b. miguel realized that american league teams tended to score more runs than national league teams during this season, possibly due to the use of designated hitters. he decides to combine separate simple random samples, one from each league, to form a stratified random sample. draw a dotplot that could represent the distribution of estimates for 10 simulations using a stratified random sample.

Explanation:

4a.

Low bias means that on average, the sampling method produces estimates that are close to the true value of the unemployment rate. The estimates are not systematically too high or too low.

4b.

Low variability means that repeated samples using the same sampling method will produce estimates that are close to each other. There is less spread in the values of the estimates.

5a.

The true - mean number of runs scored per game can be estimated as around 8. The dot - plot shows that most of the sample means cluster around 8, indicating that this is a central value in the distribution of sample means.

5b.

A stratified random sample would likely have less variability. The dot - plot for the stratified random sample would likely have the dots more closely clustered around a central value compared to the previous dot - plot. However, without specific data values, we can't draw an exact dot - plot. But it would show a more concentrated distribution of the 10 sample means from the stratified samples.

Answer:

4a.

On average, estimates are close to true value; not systematically high or low.

4b.

Repeated samples have estimates close to each other; less spread.

5a.

Around 8, as most sample means cluster there.

5b.

Dot - plot would show more concentrated distribution of sample means compared to previous one.