1. A researcher wonders about the impact of the COVID-19 pandemic on preschoolers' social skills. On a standard test of social skills development, young children's average score is 100 (=100). The researcher randomly selects a sample of 15 four-year-olds (i.e. living through the pandemic since age 2) and found their mean social skills score was 94 with a standard deviation of 8 (M=94, S=8). Test if today's preschoolers have different social skills at alpha=.01.

a) Go through the 5 steps of hypothesis testing to test if there is a difference in social skills for preschoolers living through a pandemic compared to typical preschoolers at a significance level of alpha = .01. Step 1: Identify population 1, population 2, research hypothesis, and null hypothesis. Step 2: Identify the comparison distribution, and what type of test to use. Step 3: Determine the critical cutoff. Step 4: Run the test Step 5: Make a decision (reject or fail to reject the null hypothesis) and conclude in a sentence.

b) Figure the 99% confidence interval and explain what this information tells you.

c) Figure the 95% confidence interval. Based on the calculated confidence interval (do not do further calculations) what would have been your decision/conclusion if you had conducted a hypothesis test at alpha = .05. Explain your answer (i.e. how do you know?)