Assignment 3_Stat1123

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School

Langara College *

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1123

Subject

Statistics

Date

Apr 3, 2024

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pdf

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Uploaded by AdmiralAlbatrossMaster771

STAT 1123 Assignment #3 Due: 11:59 pm on Monday Feb 13, 2023 Format: Electronic copy, submitted on D2L Important Notes about Assignment Submission: • Please note the time stamp of your submission is based on the time your file is successfully uploaded on D2L, not when you click the Send button. Please do not wait till the last few minutes to submit your work because internet connection does get cut off, computers do break down, or other unexpected events do occur when they are least expected. The onus is squarely on you if the assignment is late. No excuses. • You are allowed to submit your assignment multiple times, as long as it is before the due date/time. But earlier versions will be overwritten. In other words, only the latest submission will be kept and marked. • Late submission: There will be a 50% mark reduction per day. Assignments are not accepted by email, anytime. • Only Portable Document Format or PDF will be accepted on D2L. Your assignment will not be marked if it was submitted in another format. Hence, you will receive a mark of zero. • Please name your file in the following format: “STAT 1123_Lastname_Firstname_HW#3 .pdf”. • Please make sure all answers are in the proper order. Please have all pages or questions in the right order before submission. As much as 20% mark reduction would be incurred if this instruction is not followed closely. • Please combine all work into a single file. As much as 20% mark reduction would be incurred if this instruction is not followed closely . IF you are Mac user, make sure you are making proper pdf that is readable on D2L. You will get zero if marker can not open your file.

1. A study was conducted showing the relationship between the average maintenance cost and the age of a car in years. N umber of observations: 13 Coefficients Least Squares Standard T Parameter Estimate Error Statistic P-Value Intercept 54.7757 54.87 0.998282 0.3396 Slope 120.689 11.8442 10.1898 0.0000 Correlation Coefficient = 0.950898 R-squared = 90.4207 percent Standard Error of Est. = 80.5993 a) What is the form, direction, and strength of the correlation? [2 marks] b) What is the formula for the regression function based on the output above (Write your equation in the context of question)? [1mark] c) Interpret the slope of the regression equation (In the context of question)? [2marks]

d) Construct an 95% interval to predict the maintenance cost for a car that is 7 years old? [2 marks] e) Based on this analysis, can we conclude that a relationship exists between the maintenance cost and the age of the car in years? What is the null and alternative hypothesis? Justify your answer using three steps process. [3 marks] 2. A market research company was interested in comparing three communities A, B and C to determine whether there are any differences in their use of water filters in homes. Each of 100 homeowners sampled from each community was asked whether or not they have installed water-filtering system in their homes. Their responses (Yes or No) are summarized in the following contingency table. Use filter? Community Yes No A 62 38 B 58 42 C 73 27

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a) Clearly state the null and alternative hypotheses in this problem. [2 marks] b) Calculate the expected count for the bottom right cell (i.e., Community ‘C’ and ’No’), and explain what the number means. [2 marks] c) The Chi-square statistic has been calculated to be 13.22. What can we conclude from this finding? [2 marks] 3. The following data shows promotion data from the Vancouver police department. Gender Promotion Status Male Female Promoted 288 36 Not Promoted 672 204 a) What is the probability of getting promoted within the department? [1 mark]

b) Given that a randomly selected officer was promoted, what is the probability that the selected officer is female? [1 mark] c) What is the probability of being promoted and being male? [1 mark] d) What is the probability of being promoted or being female? [1 mark] e) Given that a randomly selected officer was female, what is the probability that they will be promoted? [1 mark]