M2209 Lab 1 TO POST

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York University *

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2209

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Mathematics

Date

Apr 3, 2024

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pdf

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2

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The materials you receive and submit for this course are to be used for this course only. You do not have permission to upload the course materials you receive to any external websites, nor to share with individuals who are not registered in this course. Materials on this site are copyright protected, and available for educational purposes within this course only. MATH2209 Lab 1 Question 1 a. QUESTION 1 The populations of this study are all fall and all spring burned blueberry patches in the province. b. QUESTION 2 The sample for this study is the 20 chosen blueberry patches. c. QUESTION 3 The individual units being measured are blueberry patches. d. QUESTION 4 The response variable is the weight of blueberries. e. QUESTION 5 The explanatory variable is the time of burn. f. QUESTION 6 This study is an example of an observational study. Question 2 a. QUESTION 7 Explain why this distribution is most likely skewed to the right. This distribution is likely skewed to the right since people could spend a lot more than $30, but cannot spend less than $0. b. QUESTION 8 Explain why you cannot draw a sampling distribution model for the average amount spent by a random sample of 18 customers. With a sample of 18, we cannot draw the sampling model because the distribution is skewed to the right c. Will the assumptions for the central limit theorem hold? Explain in the context of the question. QUESTION 9 Independence Assumption: Randomization condition: met, since we have a random sample of customers from the population of all Sunday customers. 10% (big population) condition: met, as long as there are 500 (50*10) customers now and in the future. QUESTION 10 Sample size assumption: Large enough sample condition: with n = 50, this is > 40 so large enough to assume that the sample means are approximately normal, regardless of the shape of the distribution of the amount spent by Sunday customers.
The materials you receive and submit for this course are to be used for this course only. You do not have permission to upload the course materials you receive to any external websites, nor to share with individuals who are not registered in this course. Materials on this site are copyright protected, and available for educational purposes within this course only. d. QUESTION 11 What are the mean and standard deviation for the average amount spent on Sunday by a random sample of 50 customers? Round the standard deviation to three places after the decimal. Mean ( 𝝁𝝁 𝒚𝒚 � ) = $30 Standard deviation (SD( 𝒚𝒚 � )) = 𝝈𝝈 √𝒏𝒏 ⁄ = 20/ √𝟓𝟓𝟓𝟓 = 2.828 e. QUESTION 12 Using your answers from the previous question and the 68-95-99.7 rule, label a normal curve below. f. QUESTION 13 If we were to take a random sample of 45 customers, would the interval containing the middle 68% of values be wider or narrower than the one found in part (e)? Explain. The interval would be wider than what was found above. This happens because the smaller the sample size, the more variance there is from the population mean. [OR: Show math. Standard deviation (SD( 𝒚𝒚 � )) = 𝝈𝝈 √𝒏𝒏 ⁄ = 20/ √𝟒𝟒𝟓𝟓 = 2.981, which is more than 2.828] Question 3 a. QUESTION 15 Does it appear to follow a normal model? Why or why not? No, it is not a normal model because it is not symmetric and[or] there are [possible] outliers. b. QUESTION 16 Would the central limit theorem hold? Explain. No, since the distribution is not normal, and the sample size assumption does not hold since there are [possible] outliers [we would need to take a sample of more than 40].
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