Download Math Homework: Hypothesis Testing and Statistical Significance and more Assignments Statistics in PDF only on Docsity! UNIT 7 HOMEWORK Math 102 & Core 143 Note: All data below is ficticious. 1. A monkey is given a 40 question multiple choice test, each question has 1 correct answer and 3 wrong answers. We wish to test H0 : The monkey does no better than random versus HA : The monkey knows some answers. After the test is scored it is found that the monkey answered 13 questions correctly. Do we reject the null hypothesis at a significance level of 5%? 2. Two hundred college students are selected at random. Half of them, group S are told that they must sleep 8 hours a night for the entire semester. The other half, group N are told they may sleep only 2 hours a night for the entire semester. After the semester, the average GPA for the semester for each group is calculated with the following results: AD = 2.75 with a SD = 1.1 AN = 2.95 with a SD = .95. Is the di!erence between the GPA’s highly statistically significant (i.e., at a significance level of 1%) or can it be due to variation in sampling? 3. In a far-o! world where Barbarella lives, you have found a 7-sided die. On Planet Earth 7-sided dice are necessarily biased, i.e., not all sides can be equally likely. You decide to bring the die back to earth and roll it 20 times to see if it is fair. You get 7 ones. At a significance level of 3% would you conclude that the die is biased? 4. Freda (who sang the 1980s hit song “(I Know) There’s Something Going On”) wants to know if she has a higher IQ than her archenemy Ti!any. Ti!any recently took 25 IQ tests and got an average score of 96.2 with an SD of 14.8. Freda, trying to one-up Ti!any, takes 26 tests and calculates that her average score was 104.9 with an SD of 21.4. At a significance level of 5%, can Freda claim a higher IQ than Ti!any? 5. We want to decide whether or not BMI (Body Mass Index) and IQ are independent. We survey 25 people and find a correlation coe"cient of .34. At a significance level of 5% would you conclude that BMI and IQ are dependent? 6. We are going to sample 42 people to determine the degree of linear correlation between vertical leap and height. We want to test H0 : r = .2 against HA : r < .2. At a significance level of 1%, what would our observed r-value need to be to reject H0?
