Graded Assignment Name: MTH413: Probability and Statistics | Unit 6 | Lesson 9: Unit Test Date: Graded Assignment Unit Test, Part 2: Statistical Inference Answer the question below. When you have finished, submit this assignment to your teacher by the due date for full credit. (10 points) 1. A farmer divided a field into 1-foot by 1-foot sections and tested soil samples from 32 randomly selected sections in the field. He finds that the mean pH level of the samples is 5.7 with a standard deviation of 0.26. Score A. Find the mean and standard deviation of the sampling distribution of all possible soil samples of size n = 32. Round to three decimal places. B. Construct a 95% confidence interval for the mean pH level of soil samples from every 1-foot by 1-foot section. Show your work. Even if you use technology, show the expression that is used to determine the margin of error for the interval. Interpret the interval in a complete sentence. C. The farmer tested soil samples from 34 randomly selected sections from another field. He found the mean pH level of those samples to be 6.1 with a standard deviation of 0.34. Construct a 95% confidence interval for the difference between the mean pH levels of all possible soil samples from both fields. Show your work. Even if you use technology, show the expression that is used to determine the margin of error for the interval. Interpret the interval in a complete sentence. Answer: Your Score 2012 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. ___ of 10 Page 1 of 1 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables Name: Date: Graded Assignment Unit Test, Part 2: Relationships Between Variables Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 24 points (Score for Question 1: ___ of 12 points) 1. The table shows the life expectancy of females and males in a sample of 10 countries. Country India Female 64 Male 62 Norway 82 77 Bolivia Ghana 66 59 62 58 Austria 82 76 South Africa United Kingdom 56 81 51 76 Myanmar 63 57 China Panama 74 77 70 72 (a) Create a scatter plot for the data on the grid. Identify any clusters or outliers. 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 1 of 4 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables (b) Use technology to find the equation of the least squares regression line, the correlation coefficient, and the coefficient of determination. Round each to three decimal places. Sketch the line in the scatter plot. Interpret the correlation coefficient and the coefficient of determination. (c) Use the equation of the least squares regression line to predict the male life expectancy in Egypt, where the female life expectancy is 72. Round to one decimal place. Answer: 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 2 of 4 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables (Score for Question 2: ___ of 8 points) 2. A company manager found the number of vacation days available and the number of vacation days taken during one year for a sample of employees as shown in the table. The equation of the regression line is a y 0.8 x 0.47 . Complete the table by finding the predicted and residual values. Round to one decimal place. Vacation Days Available x Vacation Days Taken y 7 6 14 10 6 3 21 15 18 15 10 10 10 6 18 14 8 5 12 10 Predicted Days Taken y Residual e (d) Create a residual plot for the data set on the grid below. (e) Explain whether a linear regression line is a good fit for the data set. Answer: 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 3 of 4 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables (Score for Question 3: ___ of 4 points) 3. Answer the following. a The owner of an ice-skating rental company heard that ice-skate rentals are predicted to increase a whopping 50% this year over last year. Explain why the number of increases might not be quite as whopping as it sounds. b The owner also heard that ice-skate rentals tend to increase or decrease as hot chocolates sales increase or decrease. The owner is fairly sure that ice skating doesn't make people crave hot chocolate, nor does drinking hot chocolate make people want to ice skate. What is the most likely lurking variable? Explain. Answer: 2015 K12 Inc. All rights reserved. Copying or distributing without K12's written consent is prohibited. Page 4 of 4 Graded Assignment Unit 10 Test, Part 2: t Procedures Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 12 points Two different professors teach an introductory statistics class at a local college. The table below shows the distribution of final grades they reported. We wonder if one of the professors is an \"easier\" grader. A B C D F Professor Jones 3 11 14 9 8 Professor Smith 9 12 8 4 4 A. What is the correct type of test to use for this situation? B. What are the conditions required to use this test? Have the conditions been satisfied? Explain. C. State the null and alternative hypothesis. D. What is the X^2 statistic and p-value for the test? E. At the = .05 level, what conclusion can your draw about the two professors? Graded Assignment Unit Test, Part 2: z Procedures Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 24 points (Score for Question 1: ___ of 12 points) 1. Conduct a hypothesis test for the following scenario. SHOW ALL YOUR WORK THE WAY WE DID IN CLASS! A coffee-dispensing machine is supposed to deliver 12 ounces of liquid into a large paper cup, but the costumer believes that the actual amount is less. As a test he plans to obtain a sample of 30 cups of the dispensed liquid. The mean of his sample is 11.5 ounces. The machine operates with a known standard deviation of = 1.1 ounces. Is there enough evidence at the = .05 level for him to claim the machine is broken? (Score for Question 2: ___ of 8 points) 2. In a SRS of 80 teenagers, the average number of text messages received per day is found to 50. If the standard deviation of number of texts received is known to be = 12, find the 95% confidence interval for the number of text messages received. SHOW ALL YOUR WORK THE WAY WE DID IN CLASS