Significance testing t-tests1 in the course of the thesis

Assignment Help Basic Statistics
Reference no: EM13371062

Significance Testing. T-Tests

1. In the course of the thesis work, a student develops a new approach for the solution of a prob-lem (here referred to as method B). The current state-of-the-art approach, method A, is well published in the literature and has been applied to a large standard problem set where its aver-age performance was discovered to be (and published in the main paper by the developers as) 5 with a standard deviation of 3 across the different problems in the problem set. In addition to the publication, the developers of method A also provide their code for anyone to be able to experiment with and the student decides to pick a random set of 15 problems from the standard problem set and apply both methods to these problems, resulting in the following performance numbers for method A. { 5 ,2 ,8 ,6 ,10 ,1 ,4 ,3 ,9 ,2 ,3 ,7,4 ,1 ,8 }, and the following performance numbers for the student's method B. {6 ,4 ,7 ,8 ,14 ,1 ,5 ,2 ,11 ,4 ,6 ,8 ,4 ,2 ,10 } . Looking at this data, the student discovers that it seems that method B outperforms method A and sets out to prove this using significance testing with a two-tailed 5% significance threshold. Given that both published performance results as well as the student's experimental results are available, a number of tests can be performed.

a) Use the standard t-test with the published results to evaluate the results in terms of the hypothesis that method B has a higher performance than method A. List all the steps (and formulas) involved in the test and what the result implies for the significance of the hypothesis.

b) Use the two-sample t-test with the student's results to evaluate the validity of the same hypothesis as in part a) . Again list all the steps (and formulas) involved in the test and what the result implies for the significance of the hypothesis.

c) Perform a paired-sample t-test with the student's results to perform another significance test for the same hypothesis as in part a) . Again list all the steps (and formulas) involved in the test and what the result implies for the significance of the hypothesis.

d) Discuss the difference between the tests in terms of their results and their assumptions. What do these results tell us about the application of the different tests and what does it tell us about the problem (and problem set) that the experiments were performed on (in terms of the relation between specific problems and the performance measure).

2. Performing a study on the development of body height, a student randomly measures the height of 20 persons in country A. The results turn out to be. { 1 .7 ,1 .6 ,1 .8 ,1 .9 ,1 .75 ,1 .83 ,1 .82 ,1 .65 , 1 .95 , 1.69 ,1 .82 ,1 .87 ,1 .65 ,1 .54 ,1 .98 ,1 .78 ,1 .69 ,1 .75 ,1 .62 ,1 .64 } . In the literature, a result is found that 20 years before, the average height of persons in country A was determined to be 1 .72 . Given that the acceptable threshold for significance is 5% , can this data be used to show that the average height of individuals in country A has increased in the last 20 years? (Show your calculations).
Comparing Distributions

3. Consider a sensor system for which we know that the sensor noise is normally distributed (and thus that an actual reading is taken from a normal distribution). Given an existing sensor with a known mean reading of µ = 2 .5 and a standard deviation of 0 .3 , we want to compare a new sensor to it. For the new sensor we take 10 measurements.:{2 ,3 .2 ,2 .7 ,2 .1 ,2 .8 ,3 .0 ,1 .8 ,2 .6 ,2 .2 ,2 .5 g}. Given this data we want to show that the sensors generate different data and that the new sensor is more reliable (i.e. has noise with a lower variance).

a) Evaluate whether the mean of the data sample from the new sensor is significantly different from that of data samples obtained from the original sensor. Include your calculations and the significance scores.

b) To evaluate the reliability of the new sensor, evaluate the hypothesis that the new sensor has a lower variance than the original sensor.

4. Consider a similar scenario as in problem 3 . where we have two distance sensors, A, and B, that have sensor noise that is normally distributed. Assume that the average sensor reading for both sensors is the actual distance and that we have a setup where both sensors can be applied to the same distance, and that we know that the first sensor has a standard deviation of 0 .3 . Given this, we perform a set of 10 experiments (with unknown, varying distance in each experiment) for which we get the following readings from sensor A:{2 .1 ,3 .5 ,5 .7 ,4 .2 ,8 .9 ,4 .2 ,12 .5 ,7 .4 ,9 .2 ,4 .8 } , and from sensor B: {1 .8 , 2 .5 ,6 .1 ,4 .0 ,9 .4 ,4 .7 ,11 .7 ,6 .8 ,9 .7 ,5 .1 } . Expand the principle of the paired-sample test that was covered for the t-test to the 2 test for variance and evaluate the hypothesis that the two sensors have different amounts of noise (i.e. that the second sensor does not have the same variance as the 0 .3 of the first sensor). Explain your rationale for this test and how you arrived at the distribution for the null hypothesis. Note. since in a paired test you are looking at the difference of two data items you have to be careful to correctly model the resulting distribution.

5. We want to evaluate the runtime performance of a randomized pattern recognition algorithm by comparing it to a known algorithm that has an average runtime performance of 25 with a standard deviation of 5 . To do this comparison, we pick 10 images that we can apply the algorithm to and run the randomized algorithm 15 times on each, resulting in the following 10 average run-time performances (one average per image):{23 .8 ,25 .1 ,24 .2 ,24 .6 ,25 .2 ,24 .1 ,23 .9 ,24 .4 ,24 .9 ,24 .3}.

a) Evaluate the significance of the hypothesis that the randomized algorithm has a lower average runtime than the known comparison algorithm. As before, explain and list your calculations, test choices, and conclusion drawn.

b) Evaluate whether the hypothesis that the randomized algorithm has a lower variance in the runtime than the comparison algorithm has statistically significant support in the data. As before, explain and list your calculations, test choices, and conclusion drawn.

Reference no: EM13371062

Questions Cloud

Problem 1the table below gives the annual us demand and : problem 1the table below gives the annual u.s. demand and supply schedules for pickup trucks.a.plot the demand and
Exchange economy 1 suppose that in a simple two-good : exchange economy 1. suppose that in a simple two-good exchange economy the two individuals a and b have the following
Practical exercise stock analysisthe purpose of this : practical exercise stock analysisthe purpose of this project is to familiarize you with the stock market. using
Md einstein is considering what she should do for the rest : m.d. einstein is considering what she should do for the rest of her life.she is considering becoming a brain surgeon.
Significance testing t-tests1 in the course of the thesis : significance testing. t-tests1. in the course of the thesis work a student develops a new approach for the solution of
Question 1 an accelerated life test on a large number of : question 1 an accelerated life test on a large number of batteries revealed that the mean life for a particular use
Section a question 1with an interest rate of 38 pa 1 710 : section a question 1with an interest rate of 3.8 p.a. 1 710 was earned in simple interest over 6 years. find the
1nbsp determine the value of 2nbsp simplify and write your : 1.nbsp determine the value of .2.nbsp simplify and write your solution where each variable appears only once and write
Purpose students will conduct one brief research exercise : purpose students will conduct one brief research exercise that will be written up as a research report using apa

Reviews

Write a Review

Basic Statistics Questions & Answers

  Statistics-probability assignment

MATH1550H: Assignment:  Question:  A word is selected at random from the following poem of Persian poet and mathematician Omar Khayyam (1048-1131), translated by English poet Edward Fitzgerald (1808-1883). Find the expected value of the length of th..

  What is the least number

MATH1550H: Assignment:  Question:     what is the least number of applicants that should be interviewed so as to have at least 50% chance of finding one such secretary?

  Determine the value of k

MATH1550H: Assignment:  Question:     Experience shows that X, the number of customers entering a post office during any period of time t, is a random variable the probability mass function of which is of the form

  What is the probability

MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?

  Binomial distributions

MATH1550H: Assignment:  Questions:  Let’s assume the department of Mathematics of Trent University has 11 faculty members. For i = 0; 1; 2; 3; find pi, the probability that i of them were born on Canada Day using the binomial distributions.

  Caselet on mcdonald’s vs. burger king - waiting time

Caselet on McDonald’s vs. Burger King - Waiting time

  Generate descriptive statistics

Generate descriptive statistics. Create a stem-and-leaf plot of the data and box plot of the data.

  Sampling variability and standard error

Problems on Sampling Variability and Standard Error and Confidence Intervals

  Estimate the population mean

Estimate the population mean

  Conduct a marketing experiment

Conduct a marketing experiment in which students are to taste one of two different brands of soft drink

  Find out the probability

Find out the probability

  Linear programming models

LINEAR PROGRAMMING MODELS

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd