Statistics Exam Practice Questions, Exams of Mathematics

Download Statistics Exam Practice Questions and more Exams Mathematics in PDF only on Docsity! MATH221 Final Exam (TCO 9) The hours of study and the final exam grades have this type of relationship: ŷ = 5.76(hours) + 35.31. Based on this linear regression equation, estimate the expected grade for a student spending 8 hours studying. Round your answer to two decimal places. Points : 46.08 81.39 CORRECT ANSWER 91.45 85.29 Instructor Explanation: Textbook Chapter 9, page 504, and the Week 2 Lecture (TCO 5) At a drive through window of a bank it’s found that 10 customers get served every 15 minutes. The bank’s manage is interested in finding a way to increase the number of customers that can be served. He thought that knowing the probability of serving 12 customers per 15 minutes could be helpful to him in the decision making process. Choose the best answer of the following: Points : This is an example of a Poisson probability experiment CORRECT ANSWER This is an example of a Binomial probability experiment This is neither a Poisson nor a Binomial probability experiment Not enough information to determine the type of experiment Instructor Explanation: Ch4: binomial and Poisson distribution concepts. (TCO 5) Microfracture knee surgery has a 75% chance of success on patients with degenerative knees. The surgery is performed on 5 patients. Find the probability of the surgery being successful on 3 or 4 patients? Points : 0.103516 0.659180 CORRECT Page 1 of 16 ANSWER 0.762695 0.64287 5 Instructor Explanation: Ch-4 by the Binomial distribution formula we get: P(x=3 OR x=4)=P(3)+P(4)= 0.263672 + 0.395508=0.659180 Page 2 of 16 (TCO 8) The mean hours of Internet usage by adults in the US in claimed to be 25 hours per week. A hypothesis test is performed at a level of significance of 0.05 with a P-value of 0.08. Choose the best interpretation of the hypothesis test. Points : Reject the null hypothesis; there is enough evidence to reject the claim that the mean of hours Internet usage by adults in the US is 25 hours per week. Reject the null hypothesis; there is enough evidence to support the claim that the mean hours Internet usage by adults in the US is 25 hours per week. Fail to reject the null hypothesis; there is not enough evidence to reject the claim that the mean hours of Internet usage by adults in the US is 25 hours per week. Fail to reject the null hypothesis; there is not enough evidence to support the claim that the mean hours of Internet usage by adults in the US is 25 hours per week. CORRECT ANSWER Instructor Explanation: Since the P-value is greater than the level of significance and the claim is in the null hypothesis, fail to reject the null hypothesis and conclude that there is not enough evidence to reject the claim. (TCO 8) A result of an entry level exam reveals that 22% of students fail that exam. In a hypothesis test conducted at a level of significance of 2%, a P-value of 0.0128 was obtained. Choose the best interpretation of the hypothesis test. Points : Fail to reject the null hypothesis; there is not enough evidence to reject the claim that 22% of students fail the entry level exam. Fail to reject the null hypothesis; there is not enough evidence to support the claim that 22% of students fail the entry level exam. Reject the null hypothesis; there is enough evidence to reject the claim that 22% of students fail the entry level exam. Reject the null hypothesis; there is enough evidence to support the claim that 22% of students fail the entry level exam. CORRECT ANSWER Instructor Explanation: Since the P-value is less than or equal to the level of significance and the claim is in the null hypothesis, reject the null hypothesis and conclude that there is enough evidence to reject the claim. (TCO 2) You want to buy light bulbs and you want to choose between two vendors. Vendor A’s light bulbs have a mean life time of 800 hours and a standard deviation of 175 hours. Vendor B’s light bulbs also have a mean life time of 800 hours, but a standard deviation of 225 hours. You want light bulbs that have more life time consistency, which vendor will you purchase from? Page 5 of 16 Points : Vendor A because you will be more likely get light bulbs with the same life time CORRECT ANSWER Page 6 of 16 Vendor B because you will be more likely get light bulbs with the same life time Either one because both produce light bulbs with the same mean life time. Neither one because a mean height of 800 inches is too short for a light bulb. Instructor Explanation: Textbook chapter 2 Page 82-87, week 1 lecture (TCO 4) A jar contains balls of four different colors; red, blue, yellow and green. The total balls are divides as 40% red, 35% blue, 20% yellow, and 5% green. If you are to select one ball at random. Find the expected value of your winning amount if the payments are set to be $0, $5, $25, $70 for red, blue, yellow and green ball respectively. Winning amount 0 5 25 70 Probability 40% 35% 20% 5% Points : The expected winning amount is $25.50 The expected winning amount is $14.50 The expected winning amount is $12.25 The expected winning amount is $10.25 Instructor Explanation: Chapter 4 CORRECT ANSWER (TCO 3) The grades of 20 students are listed in the stem and leaf diagram below. What is the probability of randomly selected student to have a grade more than or equal to 60 and less than or equal to 80. 4 | 4 5 | 6 8 6 | 5 7 9 7 | 1 5 7 8 8 9 8 | 0 2 5 7 8 8 9 9 | 7 Points : 0.65 Page 7 of 16 select a group of 4 male students? Points : 260 120 Page 10 of 16 504 0 210 CORRECT ANSWER Instructor Explanation: Chapter 3: 10C4 (TCO 6) Research shows that the life time of Everlast automobile tires is normally distributed with a mean value of 60,000 miles and a standard deviation of 5,000 miles. What is the probability of having a tire that lasts more than 67,000 miles? Points : 0.9192 0.0808 CORRECT ANSWER 1.40 0.079 3 Instructor Explanation: Chapter 5: normal distribution table; P(x>67,000)=P(z>1.40)=0.0808 (TCO 10) A research shows that employee salaries at company XYX, in thousands of dollars, are given by the equation y-hat= 48.5 + 2.2 a + 1.5 b where ‘a’ is the years of experience, and ‘b’ is the education level in years. In thousands of dollars, predict the salary for an employee with 10 years experience and 14 years education level. Points : 52.2 72.5 70.5 91.5 CORRECT ANSWER Instructor Explanation: Chapter 9: y-hat = 48.5 + (2.2)(10) + (1.5)(14) = 91.5 (TCO 9) The estimated value for the correlation coefficient for this graph might be Page 11 of 16 Points : -0.91 CORRECT ANSWER 0.50 0.91 - 0.5 0 Instructor Explanation: Chapter 9: Downward trend with tight dispersion Essay Question 1: (8 pts) Ho: mu >= 35(claim) years; Ha: mu<35 Essay Question 2: (4 pts) Ho: mu <= 20 minutes (claim); Ha: mu>20 it is a right-tailed test. (8 pts) student should either show the steps below, or show the process for the p-method. Step 2: n=49, x-bar = 21.5, s = 4.3, alpha = 0.01. Step 3: The critical value is z = 2.326. Step 4: The sample statistic is z = (21.25 - 20)/(4.3/sqrt(49)) = 2.03 p-value = 0.0212>0.01 Since P-Value is greater than the alpha value, the test statistic xbar=21.5 is close to the presumed population mean mu=20. It falls within the acceptance range of the null hypotheses. (4 pts) Fail to reject the null hypothesis. (4 pts) Thus, we fail to reject the claim that the average home delivery for their pizza is no more than 20 minutes. Essay Question 3: Part A)(12 pts) Answers may vary, but must discuss the assumptions: fixed number of independent trials, only two possible outcomes in each trial {S, F}, probability of success is the same for each trial, and random variable x counts the number of successful trials. Part B) (8 pts) n = 50; p = 0.20 since 5 possible answers of equal probability; Minitab: Calc>Probability distribution>Binomial: cumulative probability Page 12 of 16 Essay Question 6: (12 pts) For part A: Students should discuss which interval they used and why (z or t). They should also discuss how they solved the problem using either the formula, EXCEL, or the graphing calculator. The interval is (31.54, 38.46) using z = 2.576 in the formula. Technology should be close. Minitab: Stat>Basic Statistics >1- Sample Z (Test and Confidence Interval) For part B: (8 pts) We are 99% confident that the mean number of business transactions is between 31.54 and $38.46. Essay Question 7: (12 pts)For part A: Students should discuss which interval they used and why (z or t). They should also discuss how they solved the problem using either the formula, EXCEL, or the graphing calculator. The interval is (0.0473, 0.1027) using the formula and z = 2.576. Technology results should be close. Page 15 of 16 Minitab: Stat>Basic Statistics>1-Proportion For part B: (8 pts) We are 99% confident that the percentage of defective products is between 4.73% and 10.27%. Essay Question 8: For part A: (3 points each) mean = 22.3; median = 21.5; mode = 18; sample variance = 18.46; range = 12. Minitab: Stat> Basic Statistics> Display Descriptive Statistics>Statistics (check box all the required statistics)>enter data and Select C1 For part B: (5 points) It is possible that they did not come from a normal population since while the mean, median are close, the mode is way off. Also the distribution is definitely not nearly symmetrical or bell shaped. Page 16 of 16