Lead is a toxic metal. Some studies have shown chronic exposure to lead is associated with learning difficulties and decreased performance on achievement tests, particularly among children. Investigators are planning a study to investigate whether children who live near a lead factory have lower average IQ test scores compared to children who are not exposed to lead. For simplicity, we will refer to our population of interest (children ages 8-10 who live in homes with lead paint for at least 5 years) as "lead-exposed children."

We know that the average IQ in the population of unexposed children is 100 points with population standard deviation = 16 points.

30 lead-exposed children will be recruited for this new study. Investigators are interested in testing the null hypothesis that = 100 points against an alternative that the population average IQ is lower than 100 points in the lead-exposed children. Assume that =0.10.

Suppose that the alternative hypothesis is that the average IQ among lead-exposed children is (mu_a = _a =) 95 points.

If you decrease the alpha to 0.05, what happen to the power (holding other factors constant)?

a. Power increases. b. Power decreases. c. We cannot determine what happens to the power.