Suppose that an animal behaviorist is concerned about the effects of a nearby co

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. The animal behaviorist conducts a two-sample t-test to determine whether this sample provides significant evidence that birds near a construction site make less trips to the nest per hour. The animal behaviorist is using a 5% significance level. The test statistic is t = 1.81 with a p-value 0.04. Which of the following is an appropriate conclusion?

A) The samples provide statistically significant evidence that birds near a construction site make less trips to the nest per hour.

B)The animal behaviorist cannot use the t-test in this case because the sample sizes are too small.

C) The samples do not provide statistically significant evidence that birds near a construction site make less trips to the nest per hour.

Explanation / Answer

B) The animal behaviorist cannot use the t-test in this case because the sample sizes are too small. With such a samll sample, t test can be applied if the population is considered to be approximately normal, but the data shows strong skew and therefore requires a sample size greater than 40 or maybe even 50.

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