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NAME:__________________________
STAT 2120 Exam 2: April 7, 2011 7 PM – 9PM
This exam is closed book and closed notes but you are allowed to use the formula sheet and
tables that is provided for you. You may also use a calculator, but all other computer devices
(e.g. laptops, Ipads, etc.) are not permitted. All cell phones, ipods, and other portable electronic
devices must be turned off. We will keep track of the time on the board during the exam. You
are not permitted to work in groups or discuss the exam with anyone. The work you submit must
be your own. No questions of any kind will be taken during the exam. However, if you believe
a particular problem has a typo or error, you may bring this to my (or a TA’s) attention.
Please fill out your identifying information on the top of the scantron form now. On the right
side of your form, write and carefully bubble your UVA computing ID (the front part of your
original UVA email address, e.g., kcs6g) in the space provided. Left justify your computing ID
(i.e. leave space to the right). For each question, completely fill in the label of your answer in
the corresponding space on the scantron form. Each question is designed to have a single correct
answer. If it seems that more than one answer choice is correct, then you should select the answer choice that best answers the question. If you calculate a numerical answer, but its exact
value is not listed as a choice of answer, then you should select the listed value that is closest to
yours. Work diligently. If you are having trouble with a particular question, skip it and move
on. Then, remember to go back to the one(s) you skipped and answer them.
Print your name clearly above, sign the honor pledge below, and write out this honor pledge in
the space provided on the back of the scantron form. You have 120 minutes (2 hours) to
complete the exam. Each problem counts the same amount towards your final score.
Honor Pledge: I have neither given nor received unauthorized aid on this exam.
Signed:______________________________________________
Use the following scenario to answer questions 1 – 4.
During the 2010 National Football League (NFL) regular season, the home team won 143 of the 256 games played. Is this strong evidence of a home field advantage in professional football? Consider the data from 2010 to represent a random sample of games from the population of all NFL games ever played. Assume α = 0.05.
- State the hypotheses that would be used to complete the significance test that answers the question posed above.
a) H 0 : μ = 128 Ha: μ > 128 b) H 0 : p = 0.50 Ha: p > 0. c) H 0 : p 1 - p 2 = 0 H 0 : p 1 - p 2 ≠ 0 (where p 1 represents the proportion of home wins and p 2 represents the proportion of away wins) d) H 0 : μ 1 - μ 2 = 0 H 0 : μ 1 - μ 2 ≠ 0 (where μ 1 represents the mean number of home wins and μ 2 represents the mean number of away wins)
- If all assumptions hold, what is the value of the test statistic?
a) 0. b) 1. c) 1. d) 2.
- Based on your hypotheses, what is the critical value for your rejection region?
a) 1. b) 1. c) 1. d) 1.
- Which statement is the most appropriate conclusion that can be drawn based on your data.
a) We can conclude that playing home games causes an NFL team to win more often than not. b) Our results are not statistically significant at α = 0.05, thus we cannot conclude anything about a home field advantage. c) Our results are statistically significant at α = 0.05, thus we can conclude that the data show strong evidence that teams do have a home field advantage. d) This sample is too small to draw any conclusions about home field advantage.
Use the following scenario to answer questions 11 – 14.
A simple random sample of 15 UVA students and 25 VT students was taken and these students were asked about their daily internet usage. The sample mean of the 15 UVA students was 4. hours per day and the sample mean for the 25 VT students was 3.4 hours per day. The standard deviations calculated from the samples were 1.4 hours per day for UVA and 1.5 hours per day for VT. Neither sample exhibited extreme skewness or outliers.
- Construct a 99% confidence interval for the difference between population mean times. (Consider UVA as population 1).
a) (-0.019, 1.419) b) (-0.510, 1.910) c) (-0.614, 2.014) d) (-0.698, 2.098)
- When interpreting the confidence interval, we speak about
a) a level of confidence that the interval contains the true difference in population means. b) a probability that the difference between population means falls in the interval. c) a level of confidence about the true sample size. d) One minus the level of confidence being the percentage of intervals that capture the difference between sample means.
- If a significance test was conducted to determine if UVA students spend more time on the internet than VT students at α = 0.10, which of the following decisions is the most correct?
a) Reject the null hypothesis because my test statistic was greater than my critical value. b) Reject the null hypothesis because my p-value is greater than α. c) Do not reject the null hypothesis because the central limit theorem assumptions did not hold. d) No conclusion can be drawn because the procedures used are not robust.
- If we increased the sample sizes of each of our simple random samples to 20 students from UVA and 30 students from VT, which of the following statements is always true?
a) The 99% confidence interval for the mean difference will get narrower. b) The p-value for the hypothesis test will be more likely to provide significance evidence to reject the null hypothesis. c) Both (a) and (b) d) Neither (a) and (b)
Use the following scenario to answer questions 15 – 18.
The manufacturer of a certain type of ATM machine reports that the mean ATM withdrawal is $60. The manager of a convenience store with that manufacturer’s ATM machine thinks that
mean withdrawal from his machine is less than that amount. He obtains a simple random sample
of 36 withdrawals over the past month and finds the sample mean to be $52. Assume that the
population standard deviation is $12.
- Using α = .03, if the hypothesis test is conducted, what is non-standardized critical value?
(Hint: the critical value in terms of the data).
a) 56. b) 63. c) 55. d) 64.
- Calculate the power of this significance test if the mean withdrawal was actually $52.50.
a) 0. b) 0. c) 0. d) 0.
- If the actual population mean was $52.50, would we have committed a Type II error when using the sample mean of $52 in our hypothesis test?
a) Yes b) No c) Too close to call d) Not enough information to answer this question.
- Which of the following decreases the power of the above hypothesis test?
a) Increasing α b) Increasing the sample size c) Decreasing σ d) Increasing the value of the true mean (for example, if in question 16, our actual mean was now $55 instead of $52.50).
Use the following scenario to answer questions 23 – 25.
A sample of six sets of fraternal male/female twins is selected and their heights measured. The data is as follows in the format (Male height, Female height):
(66, 60); (77, 72); (71, 70); (69, 69); (71, 65); (72, 72)
It is hypothesized that the male twin is on average more than one inch taller than his respective sister and we are looking at whether there is enough statistical evidence to confirm this. (Hint: sm = 3.63, sf = 4.69, sD = 2.97).
- State the hypotheses you would use to complete a significance test.
a) H 0 : μD = 0 Ha: μD > 0 b) H 0 : μm - μf = 0 Ha: μm - μf > 0 c) H 0 : μ = 69 Ha: μ > 69 d) H 0 : μD = 1 Ha: μD > 1
- What is the test statistic used for this experiment?
a) 1. b) 4. c) 1. d) 2.
- What conclusion can be drawn from this test statistic if α = 0.05?
a) We have significant evidence to indicate that the male twin is more than one inch taller than his respective sister. b) We do not have significant evidence to indicate that the male twin is more than one inch taller than his respective sister. c) We have significant evidence to indicate that the male twin is the same height as his respective sister. d) Both (b) and (c) are correct.
- Which of the following statements is false?
a) As degrees of freedom get smaller, the t-distribution’s spread gets smaller. b) The t-distribution is more spread out than the standard normal. c) The t-distribution is symmetric about zero d) The t-distribution is curve never touches the x-axis.
Use the following scenario to answer questions 27 – 29.
A recent survey about telecommuting habits of government employees discovered, that out of 150 randomly selected FDA employees, 60 state that they telecommute once a week. In addition, 30 of 100 randomly selected FAA employees state that they telecommute once a week. Is there significant evidence that a difference exists between these two branches of the government?
- Provide the test statistic for this significance test.
a) 2. b) 1. c) 1. d) 5.
- What conclusion that can be drawn from this test statistic when α = 0.07?
a) We have significant evidence to indicate that a difference exists between these two branches of government in terms of telecommuting habits. b) We have do not have significant evidence of a difference between these two branches of government in terms of telecommuting habits. c) We have significant evidence to conclude that the FDA employees and the FAA employees are telecommuting exactly the same amount of days a week. d) None of the above are correct conclusions.
- Construct a 92% confidence interval for the parameter pFDA – pFAA.
a) (-0.006, 0.206) b) (-0.008, 0.208) c) (-0.019, 0.219) d) (-0.028, 0.228)
- To estimate a population proportion within 0.04 with 90% confidence with no prior knowledge of the population or sample proportion, the required sample size is
a) 256 b) 1024 c) 16 d) 64
- The electric company is considering an incentive plan to encourage its customers to pay their bills promptly. The plan is to discount the bills by 2% if the customer pays within 5 days, as opposed to the usual 25 days. As an experiment, 50 customers are offered the discount on their May bill. The amount of time each takes to pay his or her bill is recorded. The amount of time a random sample of 50 customers not offered the discount take to pay their bills is also recorded. If we were wondering if the discount plan works, what parameter should we conduct inference techniques on?
a) μ b) μ 1 - μ 2 (1 = discount plan and 2 = no discount plan) c) p d) p 1 - p 2 (1 = discount plan and 2 = no discount plan)
- In the above situation, the 2% represents
a) the sample proportion b) the p-value c) the significance level d) none of these
- In some states the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow this rule. As a test, he randomly samples 200 cars driving in the rain and counts the number of cars whose headlights are turned on. He finds this number to be 81. If we were testing the officer’s claim, what parameter should we conduct inference techniques on?
a) μ b) μ 1 - μ 2 (1 = lights on and 2 = lights off) c) p d) p 1 - p 2 (1 = lights on and 2 = lights off)
- In the above problem, the 200 refers to
a) the sample size b) the population size c) both (a) and (b) d) neither (a) nor (b)
- The Wilson Estimate for confidence intervals is most meaningful when
a) the sample proportion is close to 0. b) the sample proportion is close to 0 or 1 c) the sample size is small d) both (b) and (c)
- The following situation models the logic of a hypothesis test. An electrician uses an instrument to test whether or not an electrical circuit is defective. The instrument sometimes fails to detect that a circuit is good and working. The null hypothesis is that the circuit is not defective. The alternative hypothesis is that the circuit is defective. If the electrician rejects the null hypothesis, which of the following statements is true?
a) The circuit is definitely defective and needs to be repaired b) The electrician decides that the circuit is defective, but knows there is a chance it is not. c) The circuit is definitely not defective and does not need to be repaired. d) The electrician decides that the circuit is most likely not defective, but knows there is a chance it is defective.
