[4] A teacher believes that 85 percent of students in the class will want to go on a eld trip to the local 200. She performs a hypothesis test to determine if the percentage is the same or different from 85 percent. The teacher samples 50 students and 39 reply that they would want to go to the 200. For the hypothesis test, use a 1 percent level of signicance. First, determine what type of test this is, set up the hypothesis test, nd the p- value, and state your conclusion. [4] An interested citizen wanted to know if Democratic U.S. senators are older than Republican U.S. senators, on average. On May 26, 2018, the mean age of 30 randomly selected Republican senators was 61 years 247 days (61.675 years) with a standard deviation of 11.07 years. The mean age of 30 randomly selected Democratic senators was 61 years 257 days (61.704 years) with a standard deviation of 9.05 years. Do the data indicate that Democratic senators are older than Republican senators, on average? Test at a 5 percent level of signicance. [1] Distinguish between treatment variation and random variation in ANOVA test of means. [4] A start-up cell phone applications company is interested in determining whether household incomes are different for subscribers to three different service providers. A random sample of 25 subscribers to each of the three service providers was taken, and the annual household income for each subscriber was recorded. The partially completed ANOVA table for the analysis is shown here: Treatment 2.949.085.157 _ Error _ Total 9.271.678990 _ a. Complete the ANOVA table by lling in the missing sums of squares, the degrees of freedom for each source, the mean square, and the calculated Ftest statistic. b. Based on the sample results, can the start-up rm conclude that there is a difference in household incomes for subscribers to the three service providers? Conduct your test at the a = 0.05 level of signicance. Be sure to state a critical Fstatistic, a decision rule, and a conclusion