Question Question 7 10 pts A small research on sustainable mobility among college students compared the proportion of bike users in a random sample of 50 students at UC Irvine and in an independent random sample of 40 students at UC Santa Barbara. Among the 50 students at UCI, 30% were found to be bike users. Among the 40 students at UC Santa Barbara, 20% were found to be bike users. If the researchers wanted to use this data to construct a confidence interval for the difference between the proportions of bike users at UC Irvine and UC Santa Barbara relying on the methods that we have studied, would all the assumptions that are needed be satisfied? O Yes O No, because TUCSB UCSB < 10 No, because the two samples do not have the same size O No, because the sample of UCI students is less than 10% of the total number of UCI students

The time between failures of our video streaming service follows an exponential distribution with a mean of 20 days. Our servers have been running for 20 days, What is the probability that they will run for at least 60 days? (clarification: run for at least another 40 days given that they have been running 20 days). Report your answer to 3 decimal places.

The frequency distribution shown in the following table lists the number of hours per day a randomly selected sample of teenagers spent watching television. Where possible, determine what percent of the teenagers spent the following number of hours watching television. (Round your answers to one decimal place. If not possible, enter IMPOSSIBLE.) Hours per day OS Xc1 1<x<2 25x<3 3<x<4 4 SX<5 5SXC6 65x<7 Number of Teenagers 19 30 24 39 27 13 14 (a) less than 4 hours % (b) at least 5 hours (o at least 1 hour (d) less than 2 hours % (e) at least 2 hours but less than 4 hours () more than 3.5 hours

You are a proctor for a Data Science exam, and just gave a test to 15 students. You want to get an idea for the true standard deviation of the scores, using the scores you just recieved. Assume that the underlying score population is normally distributed. scores = c(53.62, 69.2, 81.96, 40.62, 76.24, 99.78, 94.49, 71.6, 76.95, 37.68, 37.59, 59.22, 92.44, 81.22, 63.74) Part A) Using the data stored in the variable scores , calculate a 95% confidence interval for the standard deviation of the data. Your confidence interval should be two tailed, and cut off an equal proportion of area on each side. Save the lower value as p1.lower and the upper value as p1. upper . Round your answers to two decimal places. # your code here p1.upper = NA p1.lower = NA alpha = 0.05

It's Halloween, and Ralphie has 6 large bags, each filled with a combination of 4 different kinds of candy. Each bag should have an approximately equal amounts of each flavor. But, being a buffalo, Ralphie is not sure that she spread the candy out evenly. She has asked your help to determine whether the proportions of flavors within each bag is the same. Each bag contains hundreds of pieces of candy, so we can't count them all by hand. Instead, you take a sample of 50 pieces from each bag. The table below displays the counts of each type of candy within each sample of 50 pieces: Candy A Candy B Candy C Candy D Bag 1 14 18 11 6 Bag 2 10 20 12 9 Bag 3 13 14 15 8 Bag 4 15 15 10 10 Bag 5 11 17 13 9 Bag 6 11 14 14 11 Part B) Determine whether the proportions of candy are equal by solving for the p-value of the appropriate test. Save your answer as p2.b. Round your answer to three decimal places. # your code here p2.b = NA Part E) After some thinking, Ralphie has changed her mind and believes that the candies actually follow the below proportions: PA = 0.25 PB = 0.35 Pc = 0.25 PD = 0.25 At a significance level of a = 0.05, determine if your observed samples agree with Ralphie's newly proposed proportions. Save the p-value of your calculations as p2.e.pval. Round this answer to three decimal places. Into variable p2.e, save TRUE if your data does agree with the new proportions, or FALSE if it does not. # your code here p2.e = NA p2.e.pval = NA

It's Halloween, and Ralphie has 6 large bags, each filled with a combination of 4 different kinds of candy. Each bag should have an approximately equal amounts of each flavor. But, being a buffalo, Ralphie is not sure that she spread the candy out evenly. She has asked your help to determine whether the proportions of flavors within each bag is the same. Each bag contains hundreds of pieces of candy, so we can't count them all by hand. Instead, you take a sample of 50 pieces from each bag. The table below displays the counts of each type of candy within each sample of 50 pieces: Candy A Candy B Candy C Candy D Bag 1 14 18 11 6 Bag 2 10 20 12 9 13 14 15 8 Bag 3 Bag 4 15 15 10 10 Bag 5 11 17 13 9 Bag 6 11 14 14 11 Part B) Determine whether the proportions of candy are equal by solving for the p-value of the appropriate test. Save your answer as p2.b. Round your answer to three decimal places # your code here p2.b = NA Part E) After some thinking, Ralphie has changed her mind and believes that the candies actually follow the below proportions: PA = 0.25 PR = 0.35 Pc = 0.25 PD = 0.25 At a significance level of a = 0.05, determine if your observed samples agree with Ralphie's newly proposed proportions. Save the p-value of your calculations as p2.e.pval. Round this answer to three decimal places. Into variable p2.e, save TRUE if your data does agree with the new proportions, or FALSE if it does not. # your code here p2.e = NA p2.e.pval = NA

autosave#question49050485 -2 -1 1 Answer each of the following questions about Fx). You have one submission for each question (a) Does lim fx) exist? X3 Ores ONO (b) Is Fx) continuous at x = 3? Oyes ONO (C) is f(x) differentiable at x = 32 OYes ONO (d) Does lim fex) exist? Oves ONO (e) is f*) continuous at x = 12 Yes ONO () is fx) differentiable at x = 17 Answer each of the following questions about f(x). You have one submission for each question (a) Does lim F*) exist? x-1 Ores ONO (b) is Fx) continuous at x = 12 Ores ONO (C) IS F(x) differentiable at x = 12 OYes No (d) Does lim, x) exist? Yes ONO (e) is x) continuous at x = 27 The graph of y = f(x) is shown below. dep=27270333&tags-autosave question4905048_5 Answer each of the following questions about Rx). You have one submission for each question (a) Does lim Fix) exist? Yes No -0 (b) is x) continuous at x = 0? OYes No (c) Is f(x) differentiable at x = 07 OYes No 3 2 -2 -1 1 2 3 Answer each of the following questions about Fx). You have one submission for each question. (a) Does lim F(x) exist? Yes No (b) Does lim Fx) exist? x-1" Ores ONO (c) Does lim fx) exist? Ores ONO (d) Is x) continuous at x = 12 Yes No