Unit 4 Examination MY ANSWERS

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Jan 9, 2024

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Elementary Statistics Unit 4 : Examination Page 1 Mathematics 13 Problem 1 Sierra College students enrolled in an online Elementary Statistics course were asked to participate in an anonymous online survey. The survey asked the students “ Which type of device will you primarily use to access your online course in Canvas? ”. Of the 152 students who answered this question, 20 responded “a desktop computer”, 121 responded “a laptop computer”, 6 responded “a smartphone”, and 5 responded “a tablet”. The Sierra College Mathematics Department believes that less than 5% of students enrolled in an online Elementary Statistics course primarily uses a smartphone to access their online course in Canvas. Use the data collected in the survey to conduct a hypothesis testing procedure to test this belief. What conclusion should be reached according to the results of this hypothesis test? STATE HYPOTHESIS: H0: p ≥ 5% H1: p < 5% a = 0.05 x = n ⋅ pˆ = 152 ⋅ 0.06 = 9.12 = 9 (HAS TO BE DISCRETE) P-VALUE = 0.699 SINCE 0.699 IS NOT 0.05 OR LESS WE DO NOT REJECT H0 Since, based on our p-value our decison was to not reject H0 this means that based on the hypothesis test, there isn't sufficient evidence to conclude that less than 5% of Sierra College Elementary Statistics students primarily use a smartphone to access their online course in Canvas.

Elementary Statistics Unit 4 : Examination Page 2 Mathematics 13 Problem 2 The following table displays the results from a Pew Research Center Survey of 2068 randomly selected adults throughout the United States. Their responses to the question below are separated by the individual’s age group. Age Group 18 - 29 30 - 49 50 - 64 65 + Do you think our government should do more to solve societal problems? Yes 319 478 296 153 No 137 265 262 158 (a) Is an adult’s view on whether or not our government should do more to solve societal problems independent of their age group at the 0.05 level of significance? (b) Based on the results of this survey, does a person’s age affect their view on whether or not our government should do more to solve societal problems? STATE HYPOTHESIS: H0 : The events are independent. H1 : The events are not independent. α = 0.05 P-VALUE = 0 SINCE P-VALUE IS LESS THAN 0.05 WE REJECT H0 Because of our decision to reject H0, at the 5% significance level, an adult’s view on whether or not our government should do more to solve societal problems is not independent of their age group Based on the results of this survey, a persons age does affect their view on wether or not our government shouldd o more to solve societal problems. The result tables shows us that adults in the 18-49 age rage think our government should do more to solve societal problems.

Elementary Statistics Unit 4 : Examination Page 3 Mathematics 13 Problem 3 Seven North American Green Frogs ( Rana clamitans ) had their jumping distance recorded (in mm) multiple times in a laboratory. The mean jumping distance for these frogs along with their length (measured from snout to vent in millimeters) are presented in the table below. Length of Frog 52 68 37 65 77 81 59 Mean Jumping Distance 546 673 415 659 793 814 563 (a) Determine the linear regression model that will best predict the mean jumping distance of a North American Green Frog based on the frog’s length. (b) How well does the linear regression model fit this sample data? (c) Use the linear regression model to predict the mean jumping distance of a North American Green Frog that is 48 mm in length. The linear regression model is yˆ = 9.30x + 54.2 r2 = 0.978 The linear regression model fits the sample well because the coefficient of determination r2 = 0.978 is quite close to 1. For x = 48, yˆ = 9.30 ⋅ (48) + 54.2 ≈ 500.6 This means the mean jumping distance of a North American Green Frog that is 48 mm in length is 500.6 mm.

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Elementary Statistics Unit 4 : Examination Page 4 Mathematics 13 Problem 4 QSR Magazine published the latest results of its annual quick serve restaurant drive-thru study. One aspect of the study examined the customer drive-thru wait times for various brands. The drive-thru wait times for random samples of customers at Chick-fil- A, McDonald’s, and KFC are given in the table below. Brand Customer drive-thru wait times (in seconds) Chick-fil-A 485 496 489 460 487 477 495 McDonald ’ s 356 362 343 327 369 351 350 KFC 291 269 251 283 286 294 278 Conduct a hypothesis test using  = 0.05 to determine whether the mean drive-thru wait times of customers at Chick-fil- A, McDonald’s, and KFC are all the same. Assume that drive thru wait times for each of these brands reasonably follow a normal distribution. P-VALUE = 0 SINCE THE P-VALUE IS LESS THAN 0.05 OUR DECISION IS TO REJECT H0 This means, that the mean drive-thru wait times of customers at Chick - fil - A, McDonald’s, and KFC are not all the same STATE HYPOTHESIS: H0 : All of the population means are equal. H1 : Not all of the population means are equal. Use α = 0.05

Elementary Statistics Unit 4 : Examination Page 5 Mathematics 13 Problem 5 Use the sample data collected in Problem 4 to construct all pairwise comparison confidence intervals to estimate the difference in the mean drive-thru wait times of customers at Chick-fil-A, McDonald’s, and KFC with a simultaneous confidence level of 95%. Interpret the results. 3 pairwise comparison confidence intervals individual confidence level = 1 - α = 3 0.95 ≈ 0.983 113.7 < μ1 − μ2 < 152.3 184.9 < μ1 − μ3 < 225.6 51.2 < μ2 − μ3 < 93. These results tell us that the wait times at the Chik-fil-A drive thru are anywhere from 113.7 to 152.3 seconds more than Mcdonalds and anywhere from 184.9 to 225.6 seconds more than KFC. We can also conclude that Mcdonalds drive thru wait times are anywhere from 51.2 to 93.4 seconds more than KFC.

Elementary Statistics Unit 4 : Examination Page 6 Mathematics 13 Problem 6 Last year, The Marist Poll conducted a national survey of adults and found that 35% responded “A lot more difficult”, 36% responded “A little more difficult”, and 29% responded “No more difficult” to the question “How much more difficult, if at all, is it to be a Black person in this country than it is to be a White person?” . Last month, they repeated this national survey with a random sample of 9,114 adults in which 4,011 responded “A lot more difficult”, 3,007 responded “A little more difficult”, and 2,096 responded “No more difficult” to the same question. Use a Chi-Squared test to determine whether the response to this question by adults nationwide had changed significantly from a year ago. Based on this result, what conclusion should The Marist Poll reach? STATE HYPOTHESIS: H0 : All of the expected frequencies fit the observed frequencies. H1 : Not all of the expected frequencies fit the observed frequencies. Use α = 0.05 n = 4011 + 3007 + 2096 = 9114 Ei = n ⋅ pi df = c − 1 = 3 − 1 = 2 P-VALUE = 0 SINCE OUR P-VALUE IS LESS THAN 0.05 OUR DECISION IS TO REJECT H0 Based on our decision the reject H0. not all of the expected frequencies fit the observed frequencies. So, based on this result, the Marist Poll should reach the conclusionthe response to this question by adults nationwide has changed significantly from a year ago with an increase in the answer "A lot more difficult" and a decrase in the answers "A little more difficult" and "No more difficult"

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Unit 4 Examination MY ANSWERS

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