7. A study was done comparing condiment preference in a "northern" state to condiment preference in a "southern" state. (a) Complete the two-way table below that compares state location and to condiment preference. [3 pts] Ketchup Mustard Total "Northern" State 25 19 "Southern" State 15 23 (a) What is the probability that person was from a "Southern" state and preferred ketchup? Round to 3 decimal places, [2 pts] (b) What is the probability that a person was from a "Southern" state and preferred mustard? Round to 3 decimal places. [2 pts] (c) What is the probability that a person prefers ketchup given that they are from a "Southern" state? Round to 3 decimal places. [2 pts] Researchers tested the claim that people from a "Southern" state preferred mustard at a higher rate than people from a "Northern" state. They tested the claim at the 5% significance level. The standardized test statistic was z = 1.567. (d) Find the p-value for this test (be sure to draw the distribution, shade the appropriate area, and write down the calculator commands used.) [3 pts] (e) State the generic conclusion [1pts]: (f) State the conclusion in context [ 2pts]: (g) Would this test be significant at the 10% level? Explain. [2 pts]