HW10 265

.pdf

School

University of Michigan, Dearborn *

*We aren’t endorsed by this school

Course

ME 230

Subject

Industrial Engineering

Date

Apr 3, 2024

Type

pdf

Pages

2

Uploaded by MinisterEnergy9403

1 IOE 265: Probability and Statistics for Engineers Homework 10 Assigned: April 1, 2022 Due: April 8, 2022 Total Points: 50 pts Question 1 [14 pts] Professor Stirling was interested to see if the University of Michigan Men’s basketball team had a difference in average scoring per game as compared to The Ohio State. In 2021, the University of Michigan men’s basketball team scored 73.06 points per game with a standard deviation of 11.56 points over 35 games. The Ohio State men’s basketball team scored 72.78 points per game with a standard deviation of 10.57 points over 32 games. We will examine three different methods for assessing whether there is a statistically significant difference in average points scored per game between the two teams at a level of significance of 0.05 (Note: all three should arrive at the same conclusion). a) [2 pts] Write the null and alternate hypotheses for assessing whether there is a difference in the average scoring per game between the University of Michigan and The Ohio State men’s basketball teams. b) [4 pts] Find the test value for this problem. Justify why you selected the test value used. c) [2 pts] Use the traditional method to assess the hypotheses. d) [2 pts] Use the p-value method to assess the hypotheses. e) [3 pts] Use the confidence interval method to assess the hypotheses. f) [1 pt] Provide a summary statement for this hypothesis evaluation.
2 Question 2 [18 pts] An engineer examined the ultimate load (in kN) for two different types of beams as given in the table below. Assume the underlying distributions are normally distributed. Observation Number 1 2 3 4 5 6 Fiberglass Beam 33 35 34 32 31 29 Carbon Composite Beam 43 46 45 41 42 36 a) [2 pt] What are the null and alternate hypotheses for assessing if the Carbon Composite Beam has a greater ultimate load than the Fiberglass beam? b) [10 pts] Assess whether the null hypothesis should be accepted or rejected by determining the test value and comparing to the critical region. Use a level of significance of 𝛼𝛼 = 0.01 . c) [4 pts] Construct the 99% confidence interval for difference in means between the two types of beams. d) [2 pts] Does the upper limit of the interval you calculated in (c) provide the same comparison as the hypothesis test you performed in (b)? Justify your answer. Question 3 [18 pts] In this question, you will perform a small experiment to examine the reaction times to a visual vs. auditory stimulus. Go to http://cognitivefun.net/ and become familiar with the visual and auditory reaction time tests (under attentional tests) that you will use for your experiment. For your study, consider whether there is a difference in visual and auditory reaction times. In addition to evaluating the data, you should consider what these results mean in context of developing automated driving systems. a) Use 5 – 10 participants (Participants can be other class members, roommates, family, or friends). Have each person complete both the audio and visual tests. The test will ask for a minimum of 5 trials per test. Use the average value of the 5 trials for a test as the data point for that participant for the selected mode. b) In your solution: i. [3 pts] State your dependent and independent variables. Provide the levels for your independent variable(s). ii. [3 pts] Procedure. What information was provided to your participants, where did the study take place, did participants have time to practice or not, how many trials were collected for each participant, was it a within or between subjects design. iii. [9 pts] Statistical analysis. Please state your null and alternate hypotheses and show your work for determining if you will reject the null. State why you selected the statistical test you chose. Provide the table of data used in your analysis. iv. [3 pts] Discussion of results. Relate the implications of your results for developing automated driving. Provide 2 possible confounding variables for your study.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help