A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 10 books from the library, test her claim at a 0.05 level of significance.

A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 10 books from the library, test her claim at a 0.05 level of significance.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Previously, an organization reported that teenagers spend 8.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Twenty-three randomly chosen teenagers were asked how many hours per week they spend on the phone, with the following results (in hours): 8.3, 8.5, 10.5, 2.9, 6.7, 7.7, 13.8, 7.8, 8.7, 11.8, 12, 6.1, 5.4, 5.8, 8.5, 7.9, 10.1,11.1, 11.6, 12.9, 3.6, 6.4, 11.2 Perform a hypothesis test using a 3% level of significance. Step 1: State the null and alternative hypotheses. Ho: ??v H: ? v ? v (So we will be performing a Select an answer v test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. v with By the Central Limit Theorem, we know that the point estimates are Select an answer and distribution standard deviation distribution mean Step 3: Find the p-value of the point estimate. P? v? v = P(| ? ♥| ? v
A graduate student is interested in how viewing different types of scenes affects working memory. For his study, he selects a random sample of 36 adults. The subjects complete a series of working memory tests before and after walking in an urban setting. Before the walk, the mean score on the test of working memory was 9.1. After the walk, the mean score was 1.4 higher. The graduate student has no presupposed assumptions about how viewing different types of scenes affects working memory, so he formulates the null and alternative hypotheses as: H00 : μDD = 0 H11 : μDD ≠ 0 Assume that the data satisfy all of the required assumptions for a repeated-measures t test. The graduate student calculates the following statistics for his hypothesis test: Mean difference (MDD) 1.4 Estimated population standard deviation of the differences (s) 1.6 Estimated standard error of the mean differences (sMDMD) 0.2667 Degrees of freedom (df) 35 The t statistic 5.25 The critical values of t…
A student wants to see if the number of times a book has been checked out of the library in the past year and the number of pages in the book are related. She guesses that the number of times a book has been checked out of the library in the past year will be a predictor of the number of pages it has. She randomly sampled 15 books from the library, test her claim at a 0.05 level of significance. number of times checked out number of pages 13 223 45 350 49 377 30 371 3 343 7 280 17 218 7 265 20 382 23 287 1 313 30 388 20 358 2 311 40 421 The correlation coefficient: r= (round to 3 decimal places) The equation y=a+bx is: (round to 3 decimal places) y=+ x The hypotheses are: H0:ρ=0H0:ρ=0 (no linear relationship)HA:ρ≠0HA:ρ≠0 (linear relationship) (claim) Since αα is 0.05 the critical value is -2.16 and 2.16 The test value is: (round to 3 decimal places) The p-value is: (round to 3 decimal places) The decision is to reject H0H0 do not reject…
Previously, an organization reported that teenagers spend 12.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is lower. Twenty-three randomly chosen teenagers were asked how many hours per week they spend on the phone, with the following results (in hours): 10.4, 10.4, 17.3, 11.2, 10, 15.2, 9.5, 5.8, 12.5, 11.8, 7.3, 10.6, 11.5, 16.2, 16.5, 14.3, 12.3, 9.9, 13.7, 8.6, 11.3, 13, 16.5 Perform a hypothesis test using a 10% level of significance. Step 1: State the null and alternative hypotheses. Ho: pv 12.5 12.5 (So we will be performing a left-tailed Vv test.) Step 2: Assuming the null hypothesis is true, determine the features of the distribution of point estimates using the Central Limit Theorem. By the Central Limit Theorem, we know that the point estimates are t-distributed with distribution mean and distribution standard deviation Step 3: Find the p-value of the point estimate. = P(tv sv p-value = Step 4: Make a Conclusion About the nulI…
An athletic shoemaker wants to test if their new running shoe specially made for sprinting is better than the competition. To do this, they recruit 35 NCAA sprinters and time their 100-meter dash wearing the company's shoe and then time their 100-meter dash again wearing the competitor’s shoe. The difference of these times is then calculated asTimecompany.shoe−Timecompetitor.shoe. The sample mean difference in times is 0.53 seconds and the sample standard deviation is 1.1. Conduct a hypothesis test at theα=0.1 level. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in the 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 underH0. 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 theα= 0.15 level and state your conclusions in the…
Any basketball fan knows that Shaquille O'Neal, one of the NBA's most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off- season, Shag had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. Check the conditions of the Central Limit Theorem for this scenario. Calculate the number of expected successes.
A company claims that less than 30% of people who both work and live in Newcastle. A study revealed that among a random sample of 200 people working in Newcastle, 62 also lived in Newcastle. Does the sample support the company’s claim? Use a level of significance of 0.01.
At a local food processing plant, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes. A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine. It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. Use a significance level of 0.01 to test the claim that the mean time is different from 90 minutes. What is the decision? A) Reject Ho because the test statistic is in the critical region and the p-value is greater than the significance level. B) Reject Ho because the test statistic is not in the critical region and the p-value is greater than the significance level.…
At a local food processing plant, it used to take an average of 90 minutes for new workers to learn a food processing job. Recently the company installed a new food processing machine. The supervisor at the company wants to find if the mean time taken by new workers to learn the food processing procedure on this new machine is different from 90 minutes. A sample of 20 workers showed that it took, on average, 85 minutes for them to learn the food processing procedure on the new machine. It is known that the learning times for all new workers are normally distributed with a population standard deviation of 7 minutes. Use a significance level of 0.01 to test the claim that the mean time is different from 90 minutes. What is the test statistic? A) -7.01 B) -2.539 C) -3.19 D) -2.528 E) -1.96