Stats Exam 1

Find the sample standard deviation of the following data set, using the statistical functions on your calculator. 0.78 0.56 0.42 0.45 0.46 0.47 A. 0.13 B. 0.12 C. 0.52 D. 0.05

A. (0.13)

Suppose that we were going to conduct a study to determine if there is an increased risk of getting lung cancer based on whether a person smokes or not. In the group of smokers(1) , we find that 10 out of 100 get lung cancer. In the non-smokers group(2), we find that 5 out of 200 get lung cancer. What is the sample relative risk? A. 4 B. 0.1 C. 0.05 D. 0.4

A. (4)

A student is interested in studying the amount spent on rent for apartments in the Gainesville area. She takes a random sample of 100 local apartment complexes. She is interested in studying the center, shape and spread of the data. What type of graph does she make? A. dotplot B. pie chart C. bar chart D. scatterplot

A. (dotplot)

Suppose that you had the following data set. 100 200 250 275 300 Suppose that the value 100 was a typo, and it was suppose to be 500 instead. How would the value of the standard deviation change? A. It would increase. B. It would decrease. C. It would stay the same. D. Unable to be determined.

A. (It would increase)

The measure of the center represents the most common observation, or class of observations A. Mode B. Median C. Mode D. Range

A. (Mode)

The IQR: A. contains the central 50% of the data B. is the distance between Q1 and the median C. is the distance between the median and Q3 D. is the distance between the minimum and the maximum

A. (contains the central 50% of the data)

The following appeared in the magazine Financial Times, March 23,1995: "When Elvis Presley died in 1977, there were 48 professional Elvis impersonators. Today there are an estimated 7328. If that growth is projected, by the year 2016 one person in four on the face of the globe will be an Elvis impersonator." This is an example of: A. extrapolation B. misuse of cause and effect C. influential outlier

A. (extrapolation)

We will flip a balanced coin 3 times and for each toss, record whether we get a Head or a Tail. Write all possible outcomes of this experiment to find the probability that we get exactly 1 head. A. 1/3 B. 3/8 C. 1/8 D. 2/3

B. (3/8)

The binomial distribution is always continuous. A. True B. False

B. False

Measure of spread around the mean, but units are not the same as those of data points A. Mean B. Median C. Mode D. Variance

D. (Variance)

A survey asks participants if they think that the president is doing a good job or not doing a good job. If there are 650 respondents (selecting using a simple random sample) to a survey, what is the approximate margin of error? A. 0.0015 B. 0.00000237 C. 0.0392 D. 0.0300

C. (0.0392)

Find the equation of the Least Squares Regression Line if x-bar= 101 sx=2.3 y-bar = 10 sy=0.5 r= -0.9 A. y-hat = 428.14-4.14x B. y-hat = -408.14 -4.14x C. y-hat = 29.7 -0.1956x D. y-hat = -9.76+0.1956x

C. (y-hat = 29.7 -0.1956x)

A small study on sleep and income found a very strong negative correlation between the two variables. However, one of the participants in the study reported only sleeping four hours per night, which was much less than other participants, and this person had by far the highest income in the study. This is an example of: A. influential outlier B. extrapolation C. misuse of cause and effect D. No answer text provided.

A. (influential outlier)

Which of the following is not part of the five number summary? A. mean B. first quartile C. third quartile D. minimum

A. Mean

Boxplots cannot be used: A. to identify outliers in a data set B. to plot several data sets side by side C. to determine the symmetry of a data set D. to determine if a data set is bell shaped

D. (to determine if a data set is bell shaped)

Mark the following statement as True or False. "The correlation coefficient ranges from 0 to 1."

False

Distances from the data points to the measure of the center always add up to zero A. Mean B. Median C. Mode D. Variance

A. (Mean)

A track and field coach wants to analyze the effect of sports drinks on the performance of his athletes. He decides to test three brands: Powerade, Gatorade and Vitaminwater. He will have each of the athletes complete a 400 meter run and record their times. Which of the following represents a confounding variable? Mark all that apply. A. He decides to give all male athletes Gatorade and the female athletes either Powerade or Vitaminwater. B. He allows each athlete to choose their favorite drink from a cooler. C. He has some of the athletes drink the sports drink two hours before running,others one hour before running, and the rest 30 minutes before running. D. He has some of the athletes drink Gatorade two hours before running, others drink Powerade one hour before running, and the rest Vitaminwater half an hour before running. E. He has some of the athletes run in the morning, some midday and some in the afternoon. F. He has some of the athletes drink Vitaminwater and run in the morning, some drink Gatorade and run midday and some drink Powerade and run in the afternoon. G. He has all his athletes repeat the 400m on different days after having one of the three drinks - on Monday they all have Gatorade, on Wednesday Powerade and on Friday Vitaminwater.

A, D, F, G

In the Fall STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how many text messages they sent per day. The researcher decided to make the number of parties attended per week the explanatory variable and the number of text messages sent per day the response variable. The least squares regression line for this relationship is y-hat = 64.96 + 25.41x. One student attended 2 parties that week and sent 20 text messages per day. What is the residual? A. -95.78 B. 115.78 C. -553.16 D. 103.16

A. (-95.78)

A simple linear regression analysis was conducted to predict the Exam 3 score of students in STA 2023 based on their Exam 1 score. The analysis yielded the following results: y-hat = 50.57+0.4845x. Which of the following is the best description of the slope of the line? A. As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points. B. As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 50.57 points. C. As the Exam 3 score increases by 1 point, the student's Exam 1 score will increase, on average by 0.4845 points. D. As the Exam 3 score increases by 1 point, the student's Exam 1 score will increase, on average by 50.57 points.

A. (As the Exam 1 score increases by 1 point, the student's Exam 3 grade will increase, on average, by 0.4845 points.)

A social scientist is interested in studying if happiness (very happy, somewhat happy, a little happy, or not happy) is associated with their sibling status (only child, one sibling, two siblings, more than 2 siblings). Which is more naturally the explanatory variable? A. Sibling Status B. Happiness

A. (Sibling Status)

Suppose that someone sampled 100 Palm trees of the same species, all planted at the same time. They recorded the height for each tree. What shape would you expect the histogram of this data to be? A. Symmetric B. Right Skewed C. Left Skewed D. Uniform

A. (Symmetric)

For the distribution of yearly incomes for lawyers, which of the following statements is correct? HINT:Assume that lawyers incomes are right skewed. A. The mean is greater than the median, because the distribution is probably right skewed. B. The mean is less than the median, because the distribution is probably left skewed. C. The mean is less than the median, because the distribution is probably right skewed. D. The mean is equal to the median, because the distribution is probably symmetric. E. The mean is greater than the median, because the distribution is probably left skewed.

A. (The mean is greater than the median, because the distribution is probably right skewed)

What is the main disadvantage of Non-Probability Samples? A. The results can be seriously biased. B. They are expensive and time-consuming. C. The sample sizes tend to be smaller than for Probability Samples. D. There are no disadvantages to using Non-Probability Samples.

A. (The results can be seriously biased.)

What does it mean to find statistically significant results? A. We say we found statistically significant differences between treatments when the observed differences in the samples are too large to be attributed to chance, so we believe there are true differences in the populations. B. We say we found statistically significant differences between treatments when the observed differences in the samples are too small to be attributed to chance, so we believe there are true differences in the populations. C. We say we found statistically significant differences between treatments when the observed differences in the populations are too large to be attributed to chance, so we believe there are true differences in the samples. D. We say we found statistically significant differences between treatments when the observed differences in the populations are too small to be attributed to chance, so we believe there are true differences in the samples.

A. (We say we found statistically significant differences between treatments when the observed differences in the samples are too large to be attributed to chance, so we believe there are true differences in the populations.)

The following is an excerpt from a paper published in BMJ (formerly the British Medical Journal) in 1994: Charig et al undertook a historical comparison of success rates in removing kidney stones. Open surgery had a success rate of 78% (273/350) while a minimally invasive procedure called percutaneous nephrolithotomy had a success rate of 83% (289/350), an improvement over the use of open surgery. However, the success rates looked rather different when stone diameter was taken into account. This showed that, for stones of <2 cm, 93% (81/87) of cases of open surgery were successful compared with just 83% (234/270) of cases of percutaneous nephrolithotomy. Likewise, for stones of >/=2 cm, success rates of 73% (192/263) and 69% (55/80) were observed for open surgery and percutaneous nephrolithotomy respectively. The main reason why the success rate reversed is because the probability of having open surgery or percutaneous nephrolithotomy varied according to the diameter of the stones. In observational (nonrandomised) studies comparing treatments it is likely that the initial choice of treatment would have been influenced by patients' characteristics such as age or severity of condition; so any difference between treatments could be accounted for by these original factors. Such a situation may arise when a new treatment is being phased in over time. Randomised trials are therefore necessary to demonstrate any treatment effect. This is an example of Simpson's paradox because: A. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them). B. when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them). C. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them). D. when the lurking variable (age or severity of the condition) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be more successful at removing them).

A. (when the lurking variable (size of the stone) is introduced, the conclusions are reversed (percutaneous nephrolithotomy turns out to be less successful at removing them).)

A car company is testing a new type of tire. They want to determine the average stopping distance in light rain, light snow and dry conditions. They test out tires on four randomly selected cars from the lot. They want to know if the stopping distance is significantly different under the three conditions. What is the factor? A. Road conditions B. Stopping Distance C. Four cars

A. Road conditions

Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. What is the probability of an adult getting a NEG result and truly having tuberculosis? A. 0.0373 B. 0.0127 C. 0.2230 D. 0.7270

B. (0.0127)

A political scientist was interested in studying America's voting habits. So, he decided to make a least squares regression equation to predict the percentage of people that would vote for Obama in 2012 based on the percentage of people that voted for Obama in 2008. The least squares equation is y-hat = -4.599 +1.04x. The value of R-squared was 96.69%. What would be the value of r? A. 0.9669 B. 0.9833 C. -0.9669 D. -0.9833 E. 0.9349 F. -0.9349

B. (0.9833)

A confidential and voluntary survey conducted in STA 3024 in the Spring of 1999 asked the students questions about their sex life. A simple linear regression analysis was conducted to predict the number of lifetime sexual partners a student has had based on the number of sexual partners the student has had in the past year. The analysis yielded an R-squared of 27.8%. Interpret R-squared. A. 27.8% of the variability in the student's number of sexual partners in the past year is explained by the number of lifetime sexual partners the student has had. B. 27.8% of the variability in the number of sexual partners students have had in their lifetime is explained by the number of sexual partners in the past year. C. As the student's number of lifetime sexual partners increases by one, the number of sexual partners in the past year increases by 27.8%. D. As the student's number of sexual partners in the past year increases by one, the number of lifetime sexual partners increases by 27.8%.

B. (27.8% of the variability in the number of sexual partners students have had in their lifetime is explained by the number of sexual partners in the past year.)

The measure of center always has exactly 50% of the observations on either side A. Mean B. Median C. Mode D. Standard Deviation

B. (Median)

A marketing researcher is testing out new names for a hair product. She asks 40 women to pick the name of the product that they would be most likely to buy out of a list of 4 names. Could she use a dotplot to describe her results? A. yes B. No

B. (No)

A school counselor looked at the relationship between SAT scores and the amount of scholarship money received for the outgoing class of 2008. What kind of study is this? A. Survey B. Observational Study C. Experiment

B. (Observational Study)

Is smaller for distributions where the points are clustered around the middle A. Median B. Standard Deviation C. Mode D. Variance

B. (Standard deviation)

If the mean is equal to the median, which of the following is true? A. There is a mistake. The mean can not equal the median. B. The data is probably symmetric. C. The data is probably skewed. D. The data has to be bell shaped distributed.

B. (The data is probably symmetric)

When taking an exam, some students quickly answer all the questions they know how to do. If they go back and revise their answers, they start second guessing themselves and end up changing their choice from the correct answer to an incorrect one. For these students, the correlation between the amount of time spent on an exam and their grade should be: A. positive and fairly strong B. negative and fairly strong C. fairly weak

B. (negative and fairly strong)

Suppose that you are rolling a six sided dice. Let A = even What is P(Ac)? A. 1/6 B. 1/4 C. 1/2 D. 1/3

C. (1/2)

Scores on an exam follow an approximately bell shaped distribution with a mean of 76.4 and a standard deviation of 6.1 points. Approximately, what percentage of the data is between 58.1 points and 94.7 points? A. 68% B. 95% C. 99.7% D. 50%

C. (99.7%)

The athletic booster club is interested in building a new basketball stadium. They are interested in determining if there is support in the Gainesville community for this. So, they walked around after a UF basketball game and selected 2000 people. They asked each selected person if they would support an effort to build a new basketball stadium. They tried to make sure that they ask people of different ages, sex and race. Will this sample be representative of all Gainesville residents? A. Yes, since it was done at random. B. Yes, since they tried to make sure that they got people of difference age, gender and race. C. No, since this is an example of convenience sample D. Yes, since they have a very large sample.

C. (No, since this is an example of convenience sample)

The measure of the spread is affected by the most outliers A. Median B. Mean C. Range D. Variance

C. (Range)

A high positive correlation is found between college students' age and their GPA. However, if one student aged 44 with a high GPA is omitted from the study, the correlation all but disappears. This is an example of: A. extrapolation B. misuse of cause and effect C. influential outlier

C. (influential outlier)

Tests for tuberculosis like all other diagnostic tests are not perfect. QFT-G is one of such tests for tuberculosis. Suppose that for the population of adults that is taking the test, 5% have tuberculosis. The test correctly identifies 74.6% of the time adults with a tuberculosis and correctly identifies those without tuberculosis 76.53% of the time. Suppose that POS stands for the test gives a positive result and S means that the adult really has tuberculosis. Represent the "5%" using notation. A. P(S) B. P(POS) C. P(S | POS) D. P(POS | S)

D. (P(POS | S))

A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says "The evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero. Which of the following would be a correct interpretation of that statement? A. Professor McDaniel said that good researchers tend to be good teachers and vice versa. B. Professor McDaniel said that good researchers tend to be bad teachers and vice versa. C. Professor McDaniel said that bad researchers tend to be bad teachers and vice versa D. Professor McDaniel said that, among good researchers, you can find both good and bad teachers and the same thing goes for bad researchers.

D. (Professor McDaniel said that, among good researchers, you can find both good and bad teachers and the same thing goes for bad researchers.)

A track and field coach wants to analyze the effect of sports drinks on the performance of his athletes. He decides to test three brands: Powerade, Gatorade and Vitaminwater. He will have each of the athletes complete a 400 meter run and record their times. Which of the following represents a blocked design? Mark all that apply. A. He decides to give all male athletes Gatorade and the female athletes either Powerade or Vitaminwater. B. He has some of the athletes drink the sports drink two hours before running, and others one hour before running. C. He has some of the athletes drink Gatorade two hours before running, others drink Powerade one hour before running, and the rest Vitaminwater half an hour before running. D. He has some of the athletes run in the morning, some midday and some in the afternoon. E. He has some of the athletes drink Vitaminwater and run in the morning, some drink Gatorade and run midday and some drink Powerade and run in the afternoon. F. He has all his athletes repeat the 400m on different days after having one of the three drinks - on Monday they all have Gatorade, on Wednesday Powerade and on Friday Vitaminwater. G. He has all his athletes repeat the 400m on different days after having each of the three drinks - and uses randomization to determine which drink they have each day. H. He creates groups of three similar athletes after ranking them by speed, then randomly assigns one person from each group to get either Powerade, Gatorade,or Vitaminwater.

G, H