A 4pts are the conditions assumptions for using a

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(a) [4pts.] Are the conditions (assumptions) for using a confidence interval for the mean amount of ice-cream it takes for all Maria’s customers to get a brain freeze satisfied? Clearly explain your answer. The assumption for making confidence interval with known standard deviation is that ¯ X is exactly or approximately normal. In this case a random sample of size 49 (64 in form B) is enough for the central limit theorem to assure approximate normality of ¯ X . Regardless of your answer in part (1a), assume for parts (1b) through (1d) that the assumptions for constructing and using a confidence interval hold. (b) [4pts.] Compute the 85% confidence interval for the mean amount of ice-cream it takes Maria’s customers to get a brain freeze. Show your work, report the critical value, and round final answers to 2 decimal places. for an 85% CI: z * = 1 . 44 . Therefore a 85% CI with known σ is FORM A: ¯ x ± z * σ n 2 . 6 ± 1 . 44 1 . 25 49 (2 . 34 , 2 . 86). FORM B: ¯ x ± z * σ n 2 . 8 ± 1 . 44 1 . 25 64 (2 . 58 , 3 . 03). (c) [4pts.] Interpret the confidence interval in question (1b) within the context of these data. FORM A: We are 85% confident that the mean amount of ice cream necessary for Maria’s customers to get brain freeze is between 2.34 and 2.86 ounces. FORM B: We are 85% confident that the mean amount of ice cream necessary for Maria’s customers to get brain freeze is between 2.58 and 3.03 ounces. (d) [4pts.] Suppose now that Maria takes a new random sample of a different size. She computes the resulting 85% confidence interval to be (2 . 47 , 2 . 99)(form A) (2 . 70 , 3 . 15)(form B). i. What is the margin of error of the new confidence interval? Show your work and round final answer to 2 decimal places. Form A: ME = 2 . 99 - 2 . 47 2 = 0 . 26 Form B: ME = 3 . 15 - 2 . 70 2 = 0 . 23 ii. What sample size was used to compute the confidence interval? Assume the standard de- viation is as before. Show all your work. We know that ME = z * σ n . Therefore solving for n results in FORM A: n = z * × σ ME 2 = 1 . 44 × 1 . 25 0 . 26 2 = 48 . FORM B: n = z * × σ ME 2 = 1 . 44 × 1 . 25 0 . 23 2 = 62 . MAX=16
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Exam II Stat 226 Fall 2018 – FORM A : KEY Page 4 2. Magikarp’s Weight. Pok´ emon GO, the mobile game that was launched by Niantic in 2016, still remains popular today. In order to obtain a fisherman’s medal, a player needs to catch 300 big Magikarp, which is a pok´ emon based on a fish. The app displays the weight for each pok´ emon caught. Dawn, a STAT226 student, is a very hardcore Pok´ emon GO player. Dawn decided to explore the distribution of Magikarp’s weight to have an idea of how much time it will take her to get the fisherman medal. Dawn recorded the weight of the first 36 Magikarp she caught during 2018. The following is a summary of the data Dawn compiled. magikarp - Distribution of x Page 1 of 1 Distributions Weight (kg) 4 6 8 10 12 14 16 Summary Statistics Mean Std Dev N 9.6470014 2.5680101 36 For parts (2a) to (2e) assume all assumptions necessary to construct a correct confidence interval are satisfied.
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  • Spring '08
  • ABBEY
  • Statistical hypothesis testing

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