Practice-Final-STAT-1150-answers

pdf

School

University of Manitoba *

*We aren’t endorsed by this school

Course

1150

Subject

Statistics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by CountOstrichMaster908

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours Name : Student Number : I understand that cheating is a serious offence: Signature : ( In Ink ) Please place a check mark beside your section number and instructor: xx xx INSTRUCTIONS I. No texts, notes, or other aids are permitted. There are no programmable/graphing calculators, cellphones or electronic translators permitted. Scientific calculators are permitted. II. This exam has a title page, 13 pages including this cover page and one blank page for rough work. Please check that you have all the pages. You may remove the staple. III. The value of each question is indicated in the lefthand margin beside the statement of the question. The total value of all questions is 57 points. IV. Answer all questions on the exam paper in the space provided beneath the question. You may NOT put any work on the backsides of the pages as it will not be marked. V. Please do not call or e-mail your instructor to inquire about grades. They will be available on Aurora shortly after they have been marked.

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours Multiple Choice Questions 1. [1] A group of high school students were asked their favourite course. Below is a table of their preferences: Class Relative Frequency Frequency Geography 0.15 30 English 0.30 60 Chemistry 0.05 ? Band ? ? Math 0.10 ? French ? 15 How many students were surveyed? (A) 43 (B) 105 (C) 135 (D) 200 (E) 300 2. [1] Which of the following statements in false ? (A) Q1 is the median of the lower half of the data set. (B) IQR is resistant to outliers. (C) In a symmetric distribution, the mean is equal to the median. (D) IQR is half the length of the range. (E) Adding observations to the data set will necessarily change the value of the median. 3. [1] A group of 7 university students needed, on average, 6 textbooks each for the fall semester. One student who had 4 textbooks dropped out of university and another student realized they forgot to get textbooks for a class and bought 2 more. On average, how many textbooks do the students still in university have? (A) 5.50 (B) 5.71 (C) 6.67 (D) 6.86 (E) 8.00 4. [1] At one point, it was reported that Fitbit users take an average of 7049 steps per day. Assuming the step counts follow a normal distribution with a standard deviation of 350, what’s the Q1 for the average step count of a group of 12 Fitbit users? (A) 6747.500 (B) 6936.000 (C) 6981.306 (D) 7023.741 (E) 7109.490 5. [1] Which of the following has a correlation of 1? (A) Home address and distance to U of M (B) Distance travelled and amount of gas in tank (C) Amount of a 10% tip and cost of a large Pizza Hut cheese pizza (D) Time elapsed and time left in a hockey game (E) Salary and cost of vehicle

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours The next two questions ( 6 and 7 ) refer to the following: Carol’s cat Grayson likes to go outside and hunt around the neighbourhood. The amount of time he spends outside before wanting back in follows a normal distribution with mean 130 minutes and standard deviation 20 minutes. 6. [1] If Carol has to leave the house for two hours, what is the probability Grayson will want to be let in before she returns? (A) 0.3085 (B) 0.6914 (C) 0.9772 (D) 1.0000 (E) Cannot be calculated 7. [1] Carol decides to keep track of how long Grayson is outside every day for 10 days. What is the probability he is outside, on average, between 120 and 145 minutes? (A) 0.4649 (B) 0.5351 (C) 0.8944 (D) 0.9340 (E) Cannot be calculated 8. [1] The owner of the local corner store wanted to estimate the average cost of a customer’s bill by making a confidence interval. In a random sample of 16 customers, the spent an average of $38. He calculated the sampling error to be 5.7575. Assume the bills have standard deviation $14. What was the level of confidence he used? (A) 88 (B) 90 (C) 92 (D) 95 (E) 98 The next two questions ( 9 and 10 ) refer to the following: To track the improvement of her students, Mrs. Marshall gives a vocabulary test to her fifth grade class with 9 students at the start of the year and then the same test again during the last week of classes for the year. For each student she records the difference in their scores (end of year - beginning of year). The differences had an average of 10.5 with a standard deviation of 9. 9. [1] If she wanted to test whether her class improved their test score over the course of the year, what would be her hypotheses? (A) H 0 : μ d = 0 vs. H A : μ d > 10 . 5 (B) H 0 : μ d = 0 vs. H A : μ d > 0 (C) H 0 : ¯ x = 0 vs. H A : ¯ x > 0 (D) H 0 : ¯ x = 10 . 5 vs H A : ¯ x > 10 . 5 (E) H 0 : μ e - μ b = 0 vs. H A : μ e - μ b > 0

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

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours 10. [1] What is the p-value of this test? (A) 0 < p-value < .005 (B) .0005 < p-value < . 001 (C) .001 < p-value < .002 (D) .001 < p-value < .0025 (E) .0025 < p-value < .005 11. [1] The odds someone is dealt a bridge hand with no face cards is approximately 0.019. In 200 hands of bridge, what is the probability between 0.017 and 0.023 of the hands will contain no face cards? (A) 0.2351 (B) 0.2423 (C) 0.3785 (D) 0.6214 (E) 0.7324 12. [1] Two siblings get into a fight over which of them is in the most family photos. What sample size would be required to estimate the true proportion of photos each of them is in to within .05 with 98% confidence? (A) 43 (B) 103 (C) 127 (D) 542 (E) 664 13. [1] The number of apples produced by a type of apple tree follows a normal distribution with a standard deviation of 12 apples. What sample size would be required to estimate the true mean number of apples per tree to within 4 apples with 95% confidence? (A) 5 (B) 6 (C) 12 (D) 25 (E) 35 The next two questions ( 14 and 15 ) refer to the following: In a sample of 200 adults, 47 said they attended the movie theatre at least once a month. Suppose you were doing a hypothesis test to see whether the true proportion of adults that go to the movie theatres once a month is less than 25% at the α = 0 . 09 level of significance. 14. [1] What would the critical value of your test be? (A) -1.35 (B) -1.69 (C) -1.34 (D) -1.645 (E) -1.96 15. [1] What would the p-value of your test be? (A) 0.3121 (B) 0.1814 (C) 0.3085 (D) 0.1977 (E) 0.3372

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours The next two questions ( 16 and 17 ) refer to the following: Jody has been recording the sales at her ice cream store for every Saturday in the summer and fitted a regression line, as seen below. On one day, despite it being cold, there was a music festival happening right by her stand and she had many more sales that day than the rest of the summer. 16. [1] What would be a reasonable estimate of b 1 for this regression line? (A) 0.4444 (B) 0.2857 (C) 3.5000 (D) 2.2500 (E) 0.4286 17. [1] If Jody were to remove that one day from her data set, what would happen to the regression line? (A) b 0 would decrease and b 1 would decrease (B) b 0 would decrease and b 1 would increase (C) b 0 would increase and b 1 would decrease (D) b 0 would increase and b 1 would increase (E) b 0 would increase and b 1 would increase

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours Long Answer 18. The following is a table of the number of pages in 8 different textbooks as well as their prices and several sample calculations. Price ( Y ) 95.00 19.95 51.50 128.50 96.00 48.50 146.75 92.00 Pages ( X ) 600 91 200 400 521 315 800 800 SS xx = 482630 . 9 SS yy = 12660 . 91 SS xy = 60852 . 53 The least-squares regression line is given by: ˆ y = 26 . 0351 + 0 . 1261 x (a) [2] Interpret the slope of the least-squares regression line. (b) [3] Calculate the coefficient of determination. (c) [2] Interpret the coefficient of determination.

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

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours (d) [3] Calculate a 90% confidence interval for the mean price when there are 50 pages in a book. ( For this part only, you may leave your answer in equation form without simplifying ) (e) [2] If you were conducting a hypothesis test to see if the slope is different from 0, what would be the value of your test statistic?

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours 19. A scouting troop is selling chocolates as a fundraiser and are trying to see if they make more sales at the mall or going door-to-door. For 15 days this month, half the troop sells chocolates at the mall and the other half goes door-to-door. Here is a summary of their sales (in number of boxes) per session. Mall Door-to-door Mean 30 35 Std. Dev. 7 3 (a) [5] Create a 95% confidence interval for the difference in mean number of chocolate bars sold at the mall and door-to-door. (b) [2] Interpret your interval.

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours 20. [6] In an effort to make sure they have enough equipment at the gym, the facility managers note the average number of people using the cardio equipment over 20 mornings and the number of people using cardio equipment at night over 20 evenings. The gym manager is curious if less people use the cardio equipment at night than in the morning. She enters the data into R and gets the following output: Two Sample t-test data: night and morning t = -1.9346, df = 38, p-value = 0.03026 alternative hypothesis: true difference in means is less than 0 92 percent confidence interval: -Inf -0.6998362 sample estimates: mean of x mean of y 18.8 21.5 Use the output to conduct a hypothesis test on the researcher’s claim using the same level of significance as they did.

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

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours 21. A researcher wanted to know if players that play exclusively Horde, exclusively Alliance, and players that play both factions have the same average number of characters. He collected data on people from all three groups and entered the data into R and got the following results after running an ANOVA test. Df Sum Sq Mean Sq F value Pr(>F) faction 2 31.3 15.65 0.51 0.603 Residuals 52 1594.1 30.66 (a) [1] What shape do the distributions have? (b) [2] Based on the box plots, do you expect the means from each group to be the same. Why or why not? (c) [3] If you were conducting the hypothesis test, what would the null and alternate hypothesis be? (d) [2] Using the p-value and part (c) to justify your answer, would the test conclude the means are different?

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours 22. [2] State the central limit theorem. 23. [3] The amount of time it takes people to complete a form follows a uniform distribution from 5 minutes to 12 minutes. If the probability it takes someone between b minutes and 10 minutes is 0.37, what is the value of b ? 24. [2] Tell me something you learned in this class that you found interesting (relevant to statistics or otherwise).

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours [Blank Page]

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

UNIVERSITY OF MANITOBA COURSE: STAT 1150 DATE & TIME: xx, xx DURATION: 3 hours (This page will not be marked)

Practice-Final-STAT-1150-answers

Related Documents