From 74 of its restaurants, noodles & company managers collected data on per-person sales and the percent of sales due to "potstickers" (a popular food item). both numerical variables failed tests for normality, so they tried a chi-square test. each variable was converted into ordinal categories (low, medium, high) using cutoff points that produced roughly equal group sizes. at α = .05, is per-person spending independent of percent of sales from potstickers? potsticker % of sales per person spending low medium high row total low 14 6 3 23 medium 7 16 5 28 high 3 4 16 23 col total 24 26 24 74 click here for the excel data file (a) the hypothesis for the given issue is h0: percentage of sales and per-person spending are independent. yes no (b) calculate the chi-square test statistic, degrees of freedom, and the p-value. (round your test statistic value to 2 decimal places and p-value to 4 decimal places. leave no cells blank - be certain to enter "0" wherever required.) test statistic d. f. p-value (c) we reject the null and find dependence. yes no

Q.1 dr. frank needs to choose 3 students from her advanced biology course to attend a conference in hawaii. the course has 40 students. which of the following methods could dr. frank use to choose a simple, random sample of 3 students? select all that apply. 1 dr. frank could have the students line up from shortest to tallest, then use her birthdate, 2/5/39, to select 3 students from the line (the 2nd student, the 5th student, and the 39th student). 2. dr. frank could upload her class roster into a spreadsheet and use a ranom-number generating function to produce 3 random numbers. the students whose names are located in the rows with these 3 numbers on the spreadsheet would be chosen. 3. dr. frank could choose the students with the 3 highest grades in the class. 4. dr. frank could count to three, then the first students to come to the front of the classroom and grab a golden ticket from her hand would be selected. 5. dr. frank could ask all students to write their name on a card, place all of the cards in a hat, shake the hat, and then pull 3 cards out from the hat. the students whose names appear on those 3 cards will be selected. 6. dr. frank could ask for volunteers to go to the conference, then choose the first 3 students who raise their hands. q2. now, choose one of the methods that you did not select and explain why this method would not result in a simple, random sample: