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STAT 2120: Final Exam 2025 Introduction To Statistical Analysis Exam Questions With Correct Upgraded A+ Score Answers.
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Consider the variable "hair color". What would be an appropriate graphical summary to use? Select all that are appropriate.
A. Bar graph
B. Pie Chart
C. Histogram
Bar graph, pie chart
Which of the following measures spread?
A. Standard deviation
B. Median
C. Mean
Standard deviation
The parameters of the simple linear regression model are denoted by beta_0 and beta_1 for the intercept and slope respectively. The estimates of these parameters are denoted by b_0 and b_ respectively.
True or False?
True
We can use a plot of residuals against the explanatory variable to assess if the conditions for regression inference are met.
True or False?
True
For a hypothesis test using H_0: beta_1 = 0 vs H_a: beta_1 is not 0, what test statistic do we use?
A. t with n-1 degrees of freedom
B. t with n-2 degrees of freedom
C. chi-square with (r-1)(c-1) degrees of freedom
D. z
B. t with n-2 degrees of freedom
A hypothesis test for zero population slope also tests if the sample correlation is zero.
True or False?
The coefficient of determination, r^2, can be found using r^2 = Regression MS / Residual MS.
True or False?
False
r^2 = Regression SS / Total SS
The difference between multiple linear regression (MLR) and simple linear regression (SLR) is that we can have more than 1 explanatory variable in MLR.
True or False?
True
Just like SLR, the estimated coefficients for MLR is found by the method of least-squares.
True or False?
True
We find residuals from MLR just like we did in SLR; residuals are the difference between an observed response and its predicted value (y - y-hat).
True or False?
True
When carrying out a hypothesis test for beta_j in a MLR model, the t-statistic is compared with the t distribution with n-2 degrees of freedom.
True or False?
False
The t-statistic is compared with the t distribution with n-p-1 degrees of freedom (which is n-2 only for SLR).
A scatterplot can be used to show the relationship between _______.
A. two categorical variables measured on the same cases.
B. two quantitative variables measured on the same cases.
B. two quantitative variables measured on the same cases.
A study examined the relationship between average amount of sleep per night and test score on final exam for stat 2120 students last semester. What is the explanatory variable in this study?
A. average amount of sleep per night
B. stat 2120 students
C. test score on final exam
A. average amount of sleep per night
Which of the following statements give a correct interpretation of a residual?
A. A residual is the amount of change in the predicted response variable when the explanatory variable increases by 1 unit.
B. A residual is the predicted value of the response variable when the explanatory variable is 0.
C. A residual is the sum of the squares of the vertical distances of the data points from the regression line.
D. A residual is the difference between an observed value of the response variable and its predicted value based on the regression line.
D. A residual is the difference between an observed value of the response variable and its predicted value based on the regression line.
Which of the following is a problem with extrapolation?
A. Predictions are not often accurate.
B. Extrapolation may influence the interpretation of relationships among variables.
C. An association between an explanatory variable and a response variable is not evidence that changes in the explanatory variable actually cause changes in the response variable.
A. Predictions are not often accurate.
Which of the following should NOT be used when both explanatory and response variables are categorical?
A. Two way table
B. Bar graph
C. Histogram
C. Histogram
Using the eating habits of your friends and family to form an estimate of how much fast food Americans tend to eat is an example of using:
A. Convenience sample
B. Simple random sample
C. Voluntary response sample
A. Convenience sample
(It's a good idea to try and remember that your "bubble" of friends and family, from whom it's easiest to get information, is most likely not representative of Americans in general!)
A voluntary response sample is likely to have more bias than a simple random sample.
True or False?
True
(The people most motivated to respond are most likely a non-representative subset of the population you're interested in studying.)
In a completely randomized experiment, the experimental units choose which treatment to receive.
Which of the following describe independent events?
A. Drawing an Ace after drawing another card from a well-shuffled deck of 52 cards.
B. The temperature in Chicago at noon on New Year's day, for each of the next five years.
C. Rolling a '5' on a fair 6-sided die after drawing an Ace from a well-shuffled deck of 52 cards.
C. Rolling a '5' on a fair 6-sided die after drawing an Ace from a well-shuffled deck of 52 cards.
(Knowing what you drew from a deck of cards has no bearing on whether you roll a '5'.)
Events A and B are _______ if they have no outcomes in common.
A. sample space
B. disjoint
C. independent
D. complements
B. disjoint
The colors of M&M candies are blue, orange, green, brown, yellow, and red. The probability distribution associated with these colors are 0.24, 0.20, 0.16, 0.14, 0.14, and _______.
(These probabilities must add up to 1.)
The union of any collection of events is the event that at least one of the collection occurs.
True or False?
True
For any two events A and B, P(A or B) = P(A) + P(B)
True or False?
False
The equation is true only if A and B are disjoint. In general, P(A or B) = P(A) + P(B) - P(A and B).
The probability that both events A and B happen together is given by P(A and B) = P(A) P(B|A).
True or False?
True
The __________ of any collection of events is the event that all the events occur.
True or False?
False
The number of hits on a webpage is a __________
A. discrete random variable
B. continuous random variable
A. discrete random variable
(Hits can only take on whole numbers; they cannot take on all values in an interval of numbers.)
In the casino game of roulette, a gambler can bet on which of 38 numbers will be the result when the roulette wheel is spun. On a $2 bet, a gambler gains $70 (so a net profit of $68) if he or she picks the right number but loses the $2 otherwise. The distribution of the random variable X: the net gain is
What is the mean of the net gain, X?
A. 68 x 37/38 + 2 x 1/
B. - 2 x 37/38 + 68 x 1/
C. 2 x 37/38 + 68 x 1/
D. 68 x 37/38 - 2 x 1/
B. - 2 x 37/38 + 68 x 1/
(For each value of X, we multiply with its corresponding probability. Then we add all of these multiplications up.)
The word "large" in "the law of large numbers" refer to:
A. large numbers of samples
B. large number of observations in the sample
C. the size of the population mean
D. large numbers of individuals in the population
B. large number of observations in the sample
(The Law of Large Numbers refers to what happens as the sample size increases, i.e. as the number of observations in the sample becomes "large".)
Suppose X is a random variable with mean 10 and standard deviation 2, and Y is a random variable with mean 5 and standard deviation 1. Let Z = X + 3Y. The mean of Z is _____.
25
Mean of Z = mean of X + 3 x mean of Y
Select the statement(s) that is(are) true about a binomial setting. Select all that are true.
A. There are a fixed number, n, of observations.
B. The n observations are all independent.
C. Each observation falls into one of just two categories.
D. The probability of success, p, is the same for each observation.
This is best modeled with a Poisson distribution since the count is the number of students that enter during a particular period of time. There is not a fixed number of "trials" like with a binomial distribution.
What is statistical inference used for?
A. To infer conclusions about the population from data based on our population.
B. To infer conclusions about the sample from data based on our sample.
C. To infer conclusions about the sample from data based on our population.
D. To infer conclusions about the population from data based on our sample.
D. To infer conclusions about the population from data based on our sample.
A parameter is a number that describes the _______. A statistic is a number that describes a ________. Fill in the blanks.
A. population; population.
B. sample; sample.
C. sample; population.
D. population; sample.
D. population; sample.
How do we reduce the variability of a statistics from an SRS?
A. increase sample size
B. decrease sample size
A. increase sample size
Sample means are _____ variable than individual observations. Fill in the blank.
A. more
B. less
C. sometimes more
D. sometimes less
B. less
Which of the following statements is correct?
A. We use a confidence interval to estimate an unknown parameter.
B. We use a confidence interval to estimate an unknown statistic.
A. We use a confidence interval to estimate an unknown parameter.
How do we decrease the margin of error for a confidence interval for the population mean?
A. Increase the size of the population
B. Increase the level of confidence
C. Increase the population standard deviation
D. Increase the sample size
D. Increase the sample size
m = z* x sigma/sqrt(n)
True or False?
True
A p-value of 0.06 means that the effect is not practically significant
True or False?
False
P-values do not say anything about the practical significance of the results, only the statistical significance.
Very small effects can be highly significant especially when a test is based on a very large sample.
True or False?
True
Running many tests at once will probably produce some significant results by chance, even if all the null hypotheses are true.
True or False?
True
How do we increase the power of a hypothesis test?
A. increase the standard deviation
B. increase the sample size
C. decrease the significance level
B. increase the sample size
The power of a fixed level test for a particular alternative is 1 minus the probability of a Type II error or that alternative.
True or False?
True
The significance level of any fixed level test is the probability of a Type I error.
True or False?
True
A star football player is accused of deflating footballs to gain a competitive advantage. The air-pressure of footballs used by the football player is measured to see if they are inflated less, on average, with the rest of the league. The investigation concluded the footballs are less inflated than the rest of the league, when in reality, they are have the same air-pressure. What kind of error do we have here?
A. Type 1 error
