Question

Penn State extension is interested in comparing the body length southern grass cicadas and citrus cicadas. The extension collected a random sample of 20 southern grass cicadas and found that they have a mean body length of 16.22 millimeters and a standard deviation of 1.34 millimeters. A separate random sample of 20 citrus cicadas resulted in a mean body length of 13.41 millimeters and a standard deviation of .73 millimeters. What is the standard error of the difference parentheses southern grass minus citrus) between the sample means

Answer 1

The standard error between the sample mean is approximately 0.3412

Explanation:

The equation for the standard error of a difference in sample mean of equal sample sizes is given as follows;

`SE(\overline x_1 - \overline x_2)={\sqrt{(s_(1)^(2) )/(n_(1))+(s _(2)^(2))/(n_(2))}}`

The given parameters are;

The number of sample of southern grass cicadas, n₁ = 20

The mean body length of the southern grass cicadas,
`\overline x _1` = 16.22 mm

The standard deviation, s₁ = 1.34 mm

The number of sample of citrus cicadas, n₂ = 20

The mean body length of the citrus cicadas,
`\overline x _2` = 13.41 mm

The standard deviation, s₂ = 0.73 mm

`SE(16.22 - 13.41)={\sqrt{(1.34^(2) )/(20)+(0.73^(2))/(20)}} \approx 0.3412`

The standard error between the sample mean, SE ≈ 0.3412