Question

Researchers were interested in the effects of lead consumption through contaminated water in Flint, MI on intelligence in children. They sampled 25 children at the local elementary school and gave them the full-scale Wechsler Intelligence Scale for Children (WISC). In a typically developing population in the United States, the WISC has a mean of 100 and a standard deviation of 15. The researchers believed that the lead consumption that had been on-going since the water source was changed in 2014 would lead to decreased intelligence test scores for the children in Flint. When they averaged the WISC scores for the 25 children in Flint who were tested, they found a mean IQ of 93.5. What type of test should they use to test this hypothesis?

a) a dependent samples t-test
b) a z-test
c) a single sample t-test
d) an independent samples t-test

Answer 1

The correct statistical test to use in this scenario is the single sample t-test, because it is appropriate for small sample sizes and when comparing to a known population mean.

Step-by-step explanation:

The appropriate statistical test for this hypothesis would be a single sample t-test. This test is used when comparing the sample mean to a known population mean when the population standard deviation is unknown and the sample size is small (less than 30). Here, researchers have a sample of 25 children, which is less than 30, and they want to compare the Flint children's mean WISC score to the known population mean. Since they have hypothesized a direction (that lead consumption would lead to decreased intelligence test scores), the t-test would be one-tailed.