Answer to Question #319356 in Statistics and Probability for Ella

Question

Problem: A researcher is conducting a study about the effectiveness of a new product to the households in a certain Barangay. His population consists of the numbers 8, 4, 2, 1, 13, and 10. Let us list all possible sample size of 4 from this researcher and compute the mean of each sample.

1. Determine the number of sets of all possible random samples using the combination formula.

2. List all the possible samples and compute the mean of each sample.

3. Construct the sampling distribution.

4. Construct the histogram.

Answer 1

$1:\\C_{6}^{4}=15$

$3: From\,\,the\,\,table\,\,above\\P\left( \bar{x}=3.75 \right) =\frac{1}{15}\\P\left( \bar{x}=4.25 \right) =\frac{1}{15}\\P\left( \bar{x}=5 \right) =\frac{1}{15}\\P\left( \bar{x}=5.25 \right) =\frac{1}{15}\\P\left( \bar{x}=5.75 \right) =\frac{1}{15}\\P\left( \bar{x}=6 \right) =\frac{2}{15}\\P\left( \bar{x}=6.5 \right) =\frac{2}{15}\\P\left( \bar{x}=6.75 \right) =\frac{1}{15}\\P\left( \bar{x}=7 \right) =\frac{1}{15}\\P\left( \bar{x}=7.25 \right) =\frac{1}{15}\\P\left( \bar{x}=8 \right) =\frac{1}{15}\\P\left( \bar{x}=8.25 \right) =\frac{1}{15}\\P\left( \bar{x}=8.75 \right) =\frac{1}{15}\\$

4: