The Physics Department states the average final exam score for String Theory was 87. You suspect it is lower. From previous years, the population standard deviation is assumed to be 4.5. You take a random sample of 23 students and obtain the following exam scores: S = {80,95, 95, 75, 82, 54, 90, 98, 83, 91, 96, 92, 97, 81, 64, 82, 90, 85, 73, 77, 93, 95, 76}. a) Define the random variable and test an appropriate set of hypotheses to address the question of interest by calculating a p-value and interpreting its numerical value in the context of the problem. Make your conclusions at the 5% level. b) If you do not assume the population standard deviation to be 4.5, how would your results in part (a) change? Explain your reasoning. c) Explain what a Type I error would be in context of the problem.

The Physics Department states the average final exam score for String Theory was 87. You suspect it is lower. From previous years, the population standard deviation is assumed to be 4.5. You take a random sample of 23 students and obtain the following exam scores: S = {80,95, 95, 75, 82, 54, 90, 98, 83, 91, 96, 92, 97, 81, 64, 82, 90, 85, 73, 77, 93, 95, 76}. a) Define the random variable and test an appropriate set of hypotheses to address the question of interest by calculating a p-value and interpreting its numerical value in the context of the problem. Make your conclusions at the 5% level. b) If you do not assume the population standard deviation to be 4.5, how would your results in part (a) change? Explain your reasoning. c) Explain what a Type I error would be in context of the problem.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

About 10% of the population had a particular genetic mutation. 900 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 900. Round answer to 4 decimal places.
Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births. Click the icon to view the data table. The mean is μ = girl(s). (Round to one decimal place as needed.) The standard deviation is o = girl(s). (Round to one decimal place as needed.)
The following table shows the number of people that are either 18, 19, 20 or 21 years old, from a sample of 258 people. a) Complete the table. Age Number of people 18 54 19 69 20 70 21 (b Find the mean for this sample. Give your answer to at least 2 decimal places. (c Find the standard deviation for this sample. Give your answer to at least 2 decimal places.
All California 5th graders take a standardized test. The mean for the population of 5th graders is 68.9 and the standard deviation for the population is 10. What is the probability of randomly selecting a student who scored a. ≥ 85? b. less than or equal to 85? c. between 80 & 85? d. between 60 & 85?
A successful basketball player has a height of 6 feet 11 inches, or 211 cm. Based on statistics from a data set, his height converts to the z score of 5.17. How many standard deviations is his height above the mean?
The board of examiners that administers the real estate broker’s examination in a certain state found that the mean score on the test was 450 and the standard deviation was 50. If the board wants to set the passing scores so that only the top 5% of all applicants pass, what should the passing score be? Assume that the scores are normally distributed.
At 60 airports within a region, the temperature is recorded. The average temperature is 67°F, with a 5°F standard deviation. What is the z-score for 68°F?
You determine that the standard deviation for a sample of test scores is 0. This tells you that 1 all the test scores must be 0. 2 all the test scores must be the same value. 3 there is no straight-line association. 4 the mean test score must also be 0. 5 you made a mistake because the standard deviation can never be 0.
Imagine the mean women’s foot size is a 7.5 with standard deviations of 1.5. a. What percentage of women have a foot size larger than 10? b. If you select 30 people at random is it likely that any of them will have a foot size larger than 10? If so, how many?