8-1 Two-Way Tables and the Chi-Square Test for Independence: Activity 5. Many school districts are facing budget cuts, and funding pre-school programs may impact other offerings. Before making their recommendations, administrators in a large urban dis- trict take a random sample of 50 seventh graders and compare the pre-algebra achievement levels of those who attended pre-school and those who did not. (These are simplified data, based on a real study.) Pre-Algebra Achievement Pre-school 8 No Pre-school 6 Below Grade Level 6 15 At Grade Level Advanced 6 9 a. The population of interest is and the response variable is and the sample is The explanatory variable is Both variables are (circle one) quantitative categorical. This is an (circle one) experiment observational study. b. Make an appropriate graph to display the percentages below grade level, at grade level, and advanced for each pre-school group. (Hint: You will need the totals for each pre- school group.) c. Does evidence suggest that pre-algebra achievement is related to pre-school attendance? Conduct an appropriate test by following the steps below. Step 1: State the hypotheses, in context. Step 2: Are conditions for a chi-square test met? Explain, and be specific. Step 3: Compute the expected counts for each cell, the x2 test statistic, and find the p-value. Draw a picture of the sampling distribution and shade the area corresponding to the p-value. Below Grade Level At Grade Level Advanced Total Pre-school 8 6 6 20 No Pre-school 6 15 9 30 Total 14 21 15 50 Step 4: State the conclusion.