TheAmerican Trends Panel(ATP), created by the Pew Research Center, is a nationally representative panel of randomly selected U.S. adults. Wave 88 survey of the panel,"The Internet and the Pandemic", was conducted April 12-18, 2021.

One of the questions is, "How important, if at all, has the internet been for you personally during the coronavirus outbreak?"The following contingency table shows the responses to this question cross-tabulatedwith respondent's family income tier.

RELIANCE ON THE INTERNET DURING THE CORONAVIRUS OUTBREAK FAMILY INCOME Important, Not Total Not too Essential but not important important essential at all Lower income 689 326 76 35 1126 Middle income 1434 661 111 33 2239 Upper income 809 219 37 11 1076 Total 2932 1206 224 79 4441 a) (6 points) Identify the variables and state the null and alternative hypotheses of a chi-squared test of independence. b) (4 points) Find the expected count for cell (1, 1) and cell (2, 3) (that is, for cells (Lower income, Essential) and (Middle income, Not too important)). c) (7 points) Using the data in R, one obtains the test statistic X- = 71.128 Explain how to make a conclusion for the chi-squared test, using the significance level of 0.001. Interpret your conclusion in context