Question

A study of fox rabies in a country gave the following information about different regions and the occurrence of rabies in each region. A random sample of

n₁ = 16

locations in region 1 gave the following information about the number of cases of fox rabies near that location.

x₁:

Region I Data

2 9 9 9 6 8 8 1
3 3 3 2 5 1 4 6
A second random sample of

n₂ = 15

locations in region II gave the following information about the number of cases of fox rabies near that location.

x₂:

Region II Data

2 2 5 2 6 8 5 4
4 4 2 2 5 6 9
Use a calculator with sample mean and sample standard deviation keys to calculate x1 and s1 in region I, and x2 and s2 in region II. (Round your answers to two decimal places.)

x₁ =

Answer 1

To calculate x₁ and s₁ in region I, use the sample mean and sample standard deviation keys on a calculator. Follow the same steps to calculate x₂ and s₂ in region II using the given data.

Step-by-step explanation:

To calculate x₁ and s₁ in region I, we can use the sample mean and sample standard deviation keys on a calculator. The sample mean (x₁) is the average of the numbers in the data set. To calculate it, we add up all the numbers and divide by the sample size:

x₁ = (2+9+9+9+6+8+8+13+3+3+2+5+1+4+6) / 16 = 82 / 16 = 5.125

The sample standard deviation (s₁) measures the variability of the data set. To calculate it, we can use the formula:

s₁ = sqrt((∑(x - x₁)²) / (n - 1))

where ∑ represents the sum, x represents each individual data point, x₁ is the sample mean, and n is the sample size. Plugging in the values:

s₁ = sqrt((∑(x - 5.125)²) / (16 - 1))

After calculating the sum of the squared differences and dividing by 15, we take the square root to get the final result.

Similarly, to calculate x₂ and s₂ in region II, we follow the same steps using the given data:

x₂ = (2+2+5+2+6+8+5+4+4+2+2+5+6+9) / 15 = 61 / 15 = 4.07

s₂ = sqrt((∑(x - 4.07)²) / (15 - 1))