Question

Suppose that an animal behaviorist is concerned about the effects of a nearby construction site on the nesting behavior of an endangered bird. In this fictional study, suppose that nesting behavior is measured by counting the number of trips to the nest per hour for an individual bird. The animal behaviorist compares a random sample of 16 birds near the construction site to a random sample of 16 birds in an undisturbed location. The animal behaviorist sets up cameras to count the number of trips to the nest per hour for each bird. For both groups, dot plots of these counts are fairly symmetric without strong skew.

Sample Statistics

Size (n)

Mean (


)

SD (s)

Construction Site

16

5.584

1.812

Undisturbed Location

16

6.786

1.945

The standard error resulting from this sample is 0.665 and df = 30.

With df = 30 the critical T-value for a 95% confidence interval is 2.0423.

What is the 95% confidence interval for the difference in the two means (construction site minus undisturbed location)?

(-1.87, -0.54)
(-3.24, 0.84)
(-2.56, 0.16)

Answer 1

To find the 95% confidence interval for the mean difference between nesting behaviors of birds near the construction site and in an undisturbed location, we use the given standard error, degrees of freedom, and the critical T-value. The confidence interval is calculated to be (-2.56, 0.16).

Step-by-step explanation:

To find the 95% confidence interval for the difference in the two means (construction site minus undisturbed location), we will use the standard error provided, the degrees of freedom (df), and the critical T-value for a 95% confidence interval. The formula for a confidence interval is:

confidence interval = (mean difference) ± (T-value * standard error)

Given that the standard error (SE) is 0.665 and df = 30, the critical T-value for a 95% confidence interval is 2.0423, and the mean of the construction site (M1) is 5.584 while the mean of the undisturbed location (M2) is 6.786, the calculation is as follows:

mean difference = M1 - M2 = 5.584 - 6.786 = -1.202

margin of error (ME) = T-value * SE = 2.0423 * 0.665 = 1.358

The lower limit of the confidence interval is:

lower limit = mean difference - ME = -1.202 - 1.358 = -2.560

The upper limit of the confidence interval is:

upper limit = mean difference + ME = -1.202 + 1.358 = 0.156

Therefore, the 95% confidence interval is (-2.56, 0.16)