MATH 225N Final Exam 2 – Question and Answers

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MATH 225N Final Exam 2 with Answers

1. A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter ?.
2. As a result answer choices below represent different hypothesis tests. Which of the choices are right-tailed tests? Select all correct answers.
3. Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits.
4. Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7 ounces. The chef knows from experience that the standard deviation for her meatball weight is 0.5 ounces.
5. So, What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.)
6. Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds.
7. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth’s mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below.
8. A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test?
9. A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars.  Of those cars, 95 had a manual transmission.
10. A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%.
11. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. .
12. Another economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%. To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car   Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle. The following is the setup for this hypothesis test:
13. So, Becky’s statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got heads 18 times.
14. So, John owns a computer repair service. For each computer, he charges \$50 plus \$45 per hour of work. A linear equation that expresses the total amount of money John earns per computer is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope?
15. Ariana keeps track of the amount of time she studies and the score she gets on her quizzes.
16. The data are shown in the table below. Which of the scatter plots below accurately records the data?
17. Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data is y^=?0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Video Games (Minutes) 306090120 Time with Family (Minutes) 50403525. According to the line of best fit, the predicted number of minutes spent with family for someone who spent 95 minutes playing video games is 31.85. Is it reasonable to use this line of best fit to make the above prediction?
18. Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply.
19. An amateur astronomer is researching statistical properties of known stars using a variety of databases.
20. They collect the color index, or B?V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter).
21. This then allows the scientist to know the star’s temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.
22. The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places.
23. A farmer divided his piece of land into 4 equivalent groups.
24. The quality of the soil is the same across the 4 groups of land. He planted the same crop in all 4 groups of land and recorded the yield of the crop in all 4 groups for a 4 week period. Is the study observational or experimental? If it is an experiment, what is the controlled factor?
25. To test the effectiveness of a drug proposed to relieve symptoms of headache, physicians included participants for a study. They gave the drug to one group and a drug with no therapeutic effect to another group. Which group receives the placebo?
26. A doctor notes her patient’s temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data?
27. As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table for grouped data. Construct this table using four classes.
28. The histogram below displays the weights of rainbow trout (in pounds) caught by all visitors at a lake on a Saturday afternoon.
29. According to this histogram, which range of weights (in pounds) contains the lowest frequency?
30. A histogram has a vertical axis labeled Frequency and has a horizontal axis that measures six categories of rainbow trout weight (in pounds). Reading from left-to-right, the weight and frequency of each category are: 4.5 to 6.5 has frequency of 4, 6.5 to 8.5 has frequency 5, 8.5 to 10.5 has frequency 7, 10.5 to 12.5 has frequency 3, 12.5 to 14.5 has frequency 1, 14.5 to 16.5 has frequency 2.
31. Describe the shape of the given histogram. A histogram has a horizontal axis from 0 to 16 in increments of 2 and a vertical axis labeled Frequency from 0 to 10 in increments of 2. The histogram contains vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the frequency is listed second: 0, 0; 1, 0; 2, 6; 3, 6; 4, 7; 5, 6; 6, 6; 7, 6; 8, 7; 9, 6; 10, 6; 11, 6; 12, 6; 13, 7; 14, 0; 15, 0.
32. The bar graph below shows the number of boys and girls in different classes.
33. A bar graph has a horizontal axis labeled Classes and a vertical axis labeled Students from 0 to 16 in increments of 2. There are two vertical bars above each horizontal axis label, with the bar on the left representing Boys and the bar on the right representing Girls. The bars have heights as follows, with the horizontal axis label listed first and the bar heights listed second from left to right: Mrs. Brown, 10 and 15; Ms. James, 11 and 12. How many total students are in Ms. James’s class? Do not include the units in your answer.
34. The line graph shown below represents the number of TVs in a house by square footage (in hundreds of feet). According to the information above, which of the following is an appropriate analysis of square footage and TVs?
35. A line graph has an x-axis labeled Square Footage (in hundreds of feet) in increments of one, and a y-axis labeled Number of TV’s in increments of one. Beginning at the point start parentheses 6,2 end parentheses, a line increases to the point start parentheses 8.5,3 end parentheses. The line remains constant to the point start parentheses 10,3 end parentheses. The line then increases, passing through the point start parentheses 12,5 end  parentheses and continues increasing until it reaches the point start parentheses 16,6 end parentheses.
36. Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells.
37. The numbers for the games so far are listed below.
38. Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears.
39. Given the following histogram, decide if the data is skewed or symmetrical. A bar graph has a horizontal axis titled Values labeled from 2 to 18 in increments of 2 and a vertical axis titled Frequency labeled from 0 to 200 in increments of 50. 14 bars are plotted, above the numbers 2 to 16. From left to right, the heights of the bars are as follows: 1. 5. 10. 40, 75, 125, 190, 180, 130, 125, 60, 25,20, 10. All values are approximate.
40. Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?
41. The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation. A figure consists of three curves along a horizontal axis, labeled Upper A, Upper B and Upper C. Curve Upper A is short and the most spread out, curve Upper B is tall and the least spread out, and curve C is farther to the left than A.
42. Brayden tosses a coin 500 times. Of those 500 times, he observes heads a total of 416 times.
43. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the significance level.
44. Is the statement below true or false? Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs.
45. Of the following pairs of events, which pair has mutually exclusive events?
46. Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains.
47. A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x¯=77, with a margin of error of 10.
48. A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p?=0.14, with a sampling standard deviation of ?p?=0.02, who preferred reading an e-book. Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books.
49. The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches.
50. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
51. Which of the following frequency tables show a skewed data set? Select all answers that apply.
52. A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll, 216 of the 374 residents sampled from urban areas want the defending champions to win the game. In more rural areas, 304 of the 466 residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to be 0.03. What is the correct interpretation of this calculation?
53. In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants into 2 groups and gave the anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo?
54. Which of the following results in the null hypothesis ??38 and alternative hypothesis ?<38?
55. True or False:  The more shoes a manufacturer makes, the more shoes they sell.
56. Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument.
57. The answer choices below represent different hypothesis tests. Which of the choices are left-tailed tests? Select all correct answers.
58. Assume the null hypothesis, H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario.
59. Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A.
60. Hugo averages 72 words per minute on a typing test with a standard deviation of 12 words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X?N(72,12).
61. The following frequency table summarizes a set of data. What is the five-number summary?
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