Spring_2022_Homework_7

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University of California, San Diego *

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MATH 20 F

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Statistics

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Jan 9, 2024

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pdf

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Uploaded by ProfessorLightningDragonfly32

Homework 7 Spring 2022 Due June 3, 2022 @ 10:00pm PST Name: Student ID: Section: Instructions Please read the following instructions carefully: 1. Please show all notation for probability statements. 2. Box your final answers. 3. Please verify that your scans are legible. 4. Please assign pages the the questions when submitting to gradescope. 5. This assignment is due via gradescope on the due date.

Homework 7 1. A manager at a farm is curious about if the size of the Colossal Cantaloupe melons that they grow at the farm has increased. They know that last year, the average weight of the Colossal Cantaloupes that were grown on the farm was 37 pounds. They take a sample of 29 melons and with a mean of 38.4 pounds and a sample standard deviation of 5.1 pounds. Has the weight of the melons increased since last year? Let µ be the true mean weight of the Colossal Cantaloupes grown this year at the farm. Test this claim at the α = 0.05 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem). (b) Calculate the test statistic. (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic under H 0 . Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at the α = 0.05 level and state your conclusion. Page 2

Homework 7 2. The football coach wants to test if a protein shake meal supplement will improve the performance of their team over a 6 week period. 16 football players each drink a protein shake in the morning and in the evening every day for the 6 week period. They each have to complete a 100m sprint both before and after the 6 weeks. The difference in their running speed, in seconds, is computed as SPD AF T − SPD BEF , and the coach wants to see if the protein shakes have made the team faster at running the 100m. The sample mean difference from the 16 students was 0.1 seconds and the sample standard deviations was 0.13 seconds. Perform a test at the α = 0 . 10 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem). (b) Calculate the test statistic. (c) Calculate the critical value. Page 3

Homework 7 (d) Draw a picture of the distribution of the test statistic under H 0 . Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at the α = 0.10 level and state your conclusions in context of the problem. Page 4

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