Almost all high school students who intend to go to college take the SAT test. In a recenttest, the mean SAT score (in verbal and mathematics) of all students was 1020. Debbie isplanning to take this test soon. Suppose the SAT scores of all students who take this test withDebbie will have a normal distribution with a mean of 1020 and a standard deviation of 153.What should her score be on this test so that only 10% of all examinees score higher thanshe does?

Let X denotes the SAT scores of all students who take this test. Given that X follows normal…

Answered: Almost all high school students who…

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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We are trying whether, a new low fat diet actually helps obese people lose weight. 100 randomly obese people are assigned to group 1 and put on a low fat-diet. another 100 people are assigned to group 2 and put on a diet of approximately the same amount of food, but not as low in fat. After 4 months, the mean net weight loss was 9.31 pounds for group 1 with a standard deviation of 4.67 pounds, and for group 2 the mean net weight loss was 7.40 pounds with a standard deviation of 4.04 pounds. Is the low-fat diet more effective? Perform a hypothesis test at the 5% significance level a) Define Parameters and state null and alternative hypothesis b) Find test statistics c) Find p-value d) Conclusion
Suppose Professor Alpha and Professor Omega each teach Introductory Biology. You need to decide which professor to take the class from and have just completed your Introductory Statistics course. Records obtained from past students indicate that students in Professor Alpha's class have a mean score of 80% with a standard deviation of 5%, while past students in Professor Omega's Class have a mean score of 80% with a standard deviation of 10%. Decide which instructor to take for Introductory Biology using a statistical argument.
Two friends, Karen and Jodi, work different shifts for the same ambulance service. They wonder if the different shifts average different numbers of calls. Looking at past records, Karen determines from a random sample of 32 shifts that she had a mean of 4.8 calls per shift. She knows that the population standard deviation for her shift is 1.4 calls. Jodi calculates from a random sample of 40 shifts that her mean was 4.2 calls per shift. She knows that the population standard deviation for her shift is 1.1 calls. Test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.01 level of significance. Let Karen's shifts be Population 1 and let Jodi's shifts be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
An English teacher has been teaching a sixth grade composition class for many years. He has the feeling that over the past several years, the writing ability of students has changed. A national test of proficiency in composition was administered 5 years ago. The resulting distribution of scores was normally shaped, had a mean of 85 and a standard deviation of 10.9. In order to test his feeling, he gives his present class of 43 students the same proficiency test. The resulting mean is 80 and the standard deviation is 8.7. a. What is the alternative hypothesis? b. What is the null hypothesis? c. What is your conclusion, using á = 0.052 tail? d. What type error may you be making because of your conclusion in part c?
Logan and Brian began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Logan took a test in Art History and earned a 76.8, and Brian took a test in English and earned a 68.9. Use the fact that all the students' test grades in the Art History class had a mean of 71.9 and a standard deviation of 11.6, and all the students' test grades in English had a mean of 61 and a standard deviation of 9.4 to answer the following questions.a) Calculate the z-score for Logan's test grade.z=z= [Round your answer to two decimal places.] b) Calculate the z-score for Brian's test grade.z=z= [Round your answer to two decimal places.]c) Which person did relatively better? Logan Brian They did equally well.
Researchers want to compare the relative effectiveness of two popular diets. They randomly assign each of 400 volunteers to one of two Groups: A & B. There are 200 volunteers in each group. Group A spends 6 months on Diet A. Group B spends 6 months on Diet B. At the beginning of the study, the difference in average weight between the two groups was negligible. After the study, the Group A had lost on average 7.8 pounds with a standard deviation of 13.4 pounds, while the Group B had lost on average 5.3 pounds with a standard deviation of 14.8 pounds. Determine the z-score/test statistic for a two-tailed test with significance level α = 0.05 , accurate to 2 decimal places.
Lucille, Rocio, and Cristina are all taking College Mathematics but from different professors. They all recently took a statistics exam and the exam scores were normally distributed in each of their classes. • Lucille's class had an average grade of 78 and the standard deviation was 7. Lucille earned 83.95 on the exam. • Rocio's class had an average grade of 82 and the standard deviation was 3. Rocio earned 86.5 on the exam. • Cristina's class had an average grade of 76 and the standard deviation was 4. Cristina earmed 82.8 on the exam. Since some professors give harder exams than others, these students decided to use statistics to figure out who did the best on their exam. Use the Cumulative Z-Score Table to answer the following questions. Write your answers as a percent with two decimal places. Hint • Lucille's score places her above % of her class. • Rocio's score places her above % of her class. • Cristina's score places her above % of her class.
The honors program at Brad's university only accepts students with an entrance exam score over 400. What percentage of students would be eligible if the students at Brad's school have an average exam score of 250, with a standard deviation of 80?
A statistics professor announces that 15% of the grades he gives are As. The results of the final examinations indicate that the mean score is 83, with a standard deviation of 6. What minimum score must a student get to receive an A?
A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, µ, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 80 and that the standard deviation is 15, but the psychologist has good reason to believe that the value for the mean has changed. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 88. Based on this information, complete the parts below. (a) What are the null hypothesis H. and the alternative hypothesis H₁ that should be used for the test? Ho : H₁ :0 (b) Suppose that the psychologist decides not to reject the null hypothesis. What sort of error might she be making? Type I Suppose the true mean SI score for all smokers is 80. Fill in the blanks to describe a Type I error. the hypothesis that u is (Choose…

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