Statistics for Business and Economics Exam 1 Review Exam Questions with Answers.

Statistics for Business and Economics: Exam 1 Review Exam Questions with Answers When all possible subsets have an equal chance of becoming the sample, the sample is referred to as a - Correct Answers: Simple Random Sample The relative frequency for a particular category is the number of times the category appears in the data. - Correct Answers: False By definition, a simple random sample of size n is any sample that is selected in a manner to guarantee every individual in the population has an equal chance of selection. - Correct Answers: False Increasing sample size will generally eliminate bias in a sample. - Correct Answers: False The entire collection of individuals or objects about which information is desired is called a sample. - Correct Answers: False - Correct Answers: A data set consisting of many observations of a single characteristic is a categorical data set. - Correct Answers: False A data set is discrete if the possible values are isolated points on the number line. - Correct Answers: True A data set is multivariate if it consists only of numeric variables. - Correct Answers: False Bar charts should be used with categorical data. - Correct Answers: True Dotplots work best for small and moderate sized numerical data sets. - Correct Answers: True Access the mtcars dataset in R. What kind or variable is am? - Correct Answers: Qualitative The variance is the positive square root of the standard deviation. - Correct Answers: False Which of the following presentations would be most useful in quickly communicating how the values from a variable are distributed? - Correct Answers: Histogram One disadvantage of using the mean as a measure of center for a data set is that its value is affected by the presence of even a single outlier in the data set. - Correct Answers: True The mean is the middle value of an ordered data set. - Correct Answers: False The density of a class can be calculated by multiplying the relative frequency of the class times the class width. - Correct Answers: False A survey form solicited the following responses: I). age of respondent II). gender of respondent III). level of job satisfaction (completely dissatisfied/somewhat dissatisfied/somewhat satisfied/completely satisfied) IV). annual income - Correct Answers: II and III only Consider the following set of scores: 1, 5, 6, 7, 8, and 10. What is the median? - Correct Answers: 6.5 The Motor Trend Car Road Tests dataset from R (mtcars) comprises fuel consumption and 10 aspects of automobile design from 1973-74 models. Calculate the standard deviation of the variable weight. - Correct Answers: 0.9784574 The Motor Trend Car Road Tests dataset from R (mtcars) comprises fuel consumption and 10 aspects of automobile design from 1973-74 models. Calculate the average horsepower of the cars in this dataset. - Correct Answers: 146.7 The variable 'am' in the mtcars dataset represent the type of transmission of the vehicle. How many cars have automatic transmission? Hint: Use the table function to count the categories. - Correct Answers: 19 The mean weight of the sample in the mtcars variable is higher than the median. - Correct Answers: False In a box plot, what percentage of the observations fall in the box? - Correct Answers: 50% Which of the following measures of central tendency indicates the point that divides the upper and lower 50% of the scores? - Correct Answers: Median The CO2 dataframe contains data from an experiment on the cold tolerance of a grass species. What is the variance of the variable Type? - Correct Answers: Does not exist The CO2 dataframe contains data from an experiment on the cold tolerance of a grass species. What is the variance of the variable uptake? - Correct Answers: 116.9515 The CO2 dataframe contains data from an experiment on the cold tolerance of a grass species. What is the IQR of the uptake? - Correct Answers: 19.225 What would happen to the mean of a distribution of test scores if a teacher adds 10 points to each score? - Correct Answers: It increases by 10 points What would happen to the standard deviation of a distribution of test scores if a teacher adds 10 points to each score? - Correct Answers: It stays the same Which of the following variables is categorical? - Correct Answers: Political affiliation Which of the following visual displays could be used for a categorical variable? - Correct Answers: Bar chart Calculate the mean of the following sample: 0.6, 0.7, -2.4, 0.4, -0.8, 6.0, 8.2, 2.4 Tip: First combine the values into a vector - Correct Answers: 1.8875 Which of the following z-scores indicates the most extreme observation? - Correct Answers: -4.3 A score of 84 separated the lowest 75% of the scores from the highest 25% of the scores, and a score of 65 separates the lowest 25% of the scores from the highest 75% of the scores. What is the percentile rank of a score of 84? - Correct Answers: 75 Data collected on heights for students taking BAT 2301 has a mean of 60 and a standard deviation of 10. After doing a z-transformation on all the measurements, what will be the mean and standard deviation of the transformed scores? - Correct Answers: Mean = 0 and standard deviation = 1 If the covariance between two variables is positive, one can conclude that the correlation will be: - Correct Answers: Positive Which of the following correlations is the strongest? - Correct Answers: -.81 The variable 'qsec' in the 'mtcars' dataset in R measures the amount of time that it takes the vehicle to reach 1/4 mile in seconds. A plot of this variable and the 'wt' weight of the car shows a very strong association between these two variables. - Correct Answers: False The covariance between 'qsec' and 'wt' is - Correct Answers: -0.3054816 The correlation between 'qsec' and 'wt is - Correct Answers: -0.1747159 Now compute the bivariate statistics of 'qsec' and 'hp' the horsepower of the vehicle. What is the correlation between these two variables? - Correct Answers: -0.71 If 'qsec' is your dependent variable, what would be a better choice for independent variable? - Correct Answers: Horsepower of the car On a study related to weight loss, the correlation between the number of hours sleeping and the percentage of weight loss was found to be +0.38. The correct interpretation for this would be: - Correct Answers: There is a positive association between the variables On a study related to weight loss, the correlation between the number of hours sleeping and the percentage of weight loss was found to be +0.38. We can interpret this number by saying that sleeping more causes a higher weight loss percentage. - Correct Answers: False The 'Orange' dataset contains measurements on the growth of orange trees. 90% of the 'age' values for the trees are lower than this value - Correct Answers: 1582 The 'Orange' dataset contains measurements on the growth of orange trees. 80% of the 'age' values for the trees are higher than this value - Correct Answers: 484 In the 'Orange' dataset the values for the variable age range from 118 to 1582 days. Given the distribution of this variable, one could say that: - Correct Answers: The values are within a normal range A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test? - Correct Answers: 118 The dataset 'women' contains average heights and weights for American women aged 30-39. Calculate the z-score for the height of a woman in this sample that mesures 70 inches. - Correct Answers: 1.1180340 The 50th percentile is equal to the 2nd quartile - Correct Answers: True A standard score, or z-score, of 2.5 represents an observation that is two and a half standard deviations greater than the mean - Correct Answers: True In this sample from the 'women' dataset one can conclude that - Correct Answers: There is a strong positive relationship between height and weight A group of researcher has just run a regression and found the following values in the output: R-squared = 0.40 RSE = 5.1 Intercept = 4.4 Slope = 2.0 What would be the predicted value for someone who scored a 3 on the predictor? - Correct Answers: 10.4 The best way to visualize the relationship between a numerical response and a categorical predictor is - Correct Answers: A boxplot by group The best way to visualize the relationship between two quantitative variables is - Correct Answers: A scatterplot Use the 'ChickWeight' dataset to answer the following questions. The response variable is 'weight'. One of the possible predictors is 'Time'. What kind of variable is Time? - Correct Answers: Discrete Run a Simple Linear Regression with Time as a predictor. For each additional day of Time, weight increases by _________ grams. - Correct Answers: 8.803 Using the model you've estimated, predict the weight in grams of a chick that has lived 15 days. - Correct Answers: 159.512 Another possible predicor is 'Diet'. This is a _____________ variable. - Correct Answers: Qualitative The diet associated with the smallest weight gain is - Correct Answers: Diet 1 The Diet associated with the largest weight gain is - Correct Answers: Diet 3 The predicted weight for a chicken that has been fed Diet 4 is - Correct Answers: 135.27 Between these two models, the model with the smallest error has - Correct Answers: Time as predictor The "mtcars" dataset comprises fuel consumption and several aspects for 32 automobiles from 1973 and 1974. For this problem, the response variable is 'qsec', which measures the amount of time in seconds that it takes a car to reach ¼ of a mile, that is, we are trying to predict what makes a car go fast. Run a simple linear regression using transmission ('am') as an explanatory variable. The automatic cars are coded as 0 and the manual cars as 1. The average acceleration time that it takes automatic cars to reach that distance is - Correct Answers: 18.1832 For cars with a manual transmission you would adjust the baseline by this much - Correct Answers: -0.8232 The proportion of the variation in qsec that is explained by the transmission is - Correct Answers: 0.05284 Looking at the results of this regression, one can say that the fastest cars on average have this type of transmission - Correct Answers: Manual Now run a regression using 'vs' as your predictor. Cars with a V-shape engine are coded as 0 and cars with a straight engine are coded as 1. What is the R-squared for this model? - Correct Answers: 0.5543 Which of these explanatory variables provides a better fit for the data? - Correct Answers: vs Finally, run a simple linear regression (SLR) using horsepower 'hp' as a covariate. What is the predicted time to reach 1/4 of a mile for a car that has a horsepower of 100? - Correct Answers: 18.71055 What is the predicted time to reach 1/4 of a mile for a car that has a horsepower of 200? - Correct Answers: 16.86475 The function resid() or residuals() applied on a linear model object will print the residuals for each of the observations in the sample. Using the model you estimated with horsepower as predictor, which vehicle in the sample mtcars has the biggest error? Note: It was pointed out to me that older versions of RSudio don't show the names of the observations, only the number. If you can't find this information don't worry about it (I won't ask it on the exam) but if you can work with the latest version of the software this is the best. There is an updated version of RStudio on the Virtual Desktop Machine here at Trinity. You can access it at <>. - Correct Answers: Merc 230