Unit 4 Examination MY ANSWERS

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Sierra College *

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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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