Statistics Sample Final Exam
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Questions and Answers

Find the median of the call received on 7 consecutive days 11, 13, 17, 13, 23, 25, 19

  • 25
  • 23
  • 17
  • 13 (correct)

Which one of the following variables is not categorical?

  • Gender of a person
  • Marital status
  • Choice on a test item: true or false.
  • Age of a person. (correct)

If the values of two variables move in the opposite direction,

  • The correlation is said to be non-linear
  • The correlation is said to be positive
  • The correlation is said to be negative (correct)
  • The correlation is said to be linear

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: I = 50,000 - 8X. The above equation implies that an

<p>increase of $1 in price is associated with a decrease of $8000 in sales (A)</p> Signup and view all the answers

Calculate the range of the given sets of data 7, 47, 8, 42, 47, 95, 42, 96, 2 (formula: max - min)

<p>94 (B)</p> Signup and view all the answers

When the correlation coefficient, r, is close to one:

<p>there is a strong linear relationship between the two variables (D)</p> Signup and view all the answers

Which of the given plots is suitable for testing the linear relationship between a dependent and independent variable?

<p>Scatter plot (B)</p> Signup and view all the answers

Find the mode and median of the 9 consecutive number 7, 12, 8, 14, 21, 23, 27, 7, 11

<p>7, 12 (C)</p> Signup and view all the answers

Which of the following is a branch of statistics?

<p>Both A and B (A)</p> Signup and view all the answers

What are the variables whose calculation is done according to the weight, height, and length known as?

<p>Continuous variables (A)</p> Signup and view all the answers

The correlation coefficient is used to determine:

<p>The strength of the relationship between the x and y variables (B)</p> Signup and view all the answers

If the correlation coefficient is a positive value, then the slope of the regression line

<p>must also be positive (D)</p> Signup and view all the answers

A residual plot:

<p>displays the explanatory variable versus the response variable. (D)</p> Signup and view all the answers

If the values of two variables move in the same direction,

<p>The correlation is said to be positive (D)</p> Signup and view all the answers

Which of the following techniques is an analysis of the relationship between two variables to help provide the prediction mechanism?

<p>Regression (C)</p> Signup and view all the answers

The degree of peakedness or flatness of a unimodel distribution is called:

<p>Kurtosis (B)</p> Signup and view all the answers

What is the meaning of the testing of the hypothesis?

<p>It is a rule for acceptance or rejection of the hypothesis of the research problem (C)</p> Signup and view all the answers

What is the skewness of normal distribution?

<p>0 (C)</p> Signup and view all the answers

The measurements of spread or scatter of the individual values around the central point is called:

<p>Measures of dispersion (A)</p> Signup and view all the answers

The measure of dispersion which uses only two observations is called:

<p>Range (C)</p> Signup and view all the answers

The range of the scores 29, 3, 143, 27, 99 is:

<p>140 (A)</p> Signup and view all the answers

The average of squared deviations from mean is called:

<p>Variance (C)</p> Signup and view all the answers

Standard deviation is always calculated from:

<p>Mean (A)</p> Signup and view all the answers

In case of positively skewed distribution, the extreme values lie in the:

<p>Right tail (B)</p> Signup and view all the answers

The lower and upper quartiles of a distribution are 80 and 120 respectively, while median is 100. The shape of the distribution is:

<p>Symmetrical (A)</p> Signup and view all the answers

In a symmetrical distribution Q1 = 20 and median= 30. The value of Q3 is:

<p>40 (D)</p> Signup and view all the answers

In a normal distribution, what percentage of the data falls within one standard deviation of the mean?

<p>68% (A)</p> Signup and view all the answers

The area under the normal curve represents:

<p>Probability (B)</p> Signup and view all the answers

Which measure indicates the degree of symmetry in a probability distribution?

<p>Skewness (B)</p> Signup and view all the answers

A normal distribution is perfectly symmetrical around the:

<p>Mean (B)</p> Signup and view all the answers

What is the skewness of a perfectly symmetrical distribution?

<p>0 (A)</p> Signup and view all the answers

If a dataset has a positive skewness, it means:

<p>Its tail extends more to the right (A)</p> Signup and view all the answers

Kurtosis measures the:

<p>Tendency of a distribution's tails to be heavy or light (C)</p> Signup and view all the answers

What does a positive kurtosis value indicate about a distribution?

<p>The distribution has heavy tails (D)</p> Signup and view all the answers

In a normal distribution, what is the value of kurtosis?

<p>0 (C)</p> Signup and view all the answers

What does a leptokurtic distribution indicate?

<p>Heavy-tailed distribution (D)</p> Signup and view all the answers

What is the probability of an event that is certain to occur?

<p>1 (C)</p> Signup and view all the answers

What does the central limit theorem state about the distribution of sample means?

<p>They will approach a normal distribution as sample size increases (C)</p> Signup and view all the answers

Which of the following is NOT a characteristic of a normal distribution?

<p>Long tails on either side (B)</p> Signup and view all the answers

What is the main purpose of statistics?

<p>Summarize and analyze data (A)</p> Signup and view all the answers

Which of the following represents a population parameter?

<p>Standard deviation of a population (A)</p> Signup and view all the answers

The process of selecting a subset of individuals from a population is called:

<p>Sampling (D)</p> Signup and view all the answers

What is the branch of statistics concerned with drawing conclusions from data?

<p>Inferential Statistics (A)</p> Signup and view all the answers

The probability of an impossible event is:

<p>0 (B)</p> Signup and view all the answers

If two events cannot happen at the same time, they are called:

<p>Mutually Exclusive (D)</p> Signup and view all the answers

The sum of probabilities of all possible outcomes of an experiment is:

<p>1 (A)</p> Signup and view all the answers

In a fair coin toss, what is the probability of getting heads?

<p>0.5 (A)</p> Signup and view all the answers

What is the probability of rolling a 4 on a fair six-sided die?

<p>1/6 (D)</p> Signup and view all the answers

Which measure of central tendency is most affected by extreme values?

<p>Mean (A)</p> Signup and view all the answers

The spread of data in a dataset is measured by

<p>Standard deviation (B)</p> Signup and view all the answers

What is the mode of the dataset {2, 3, 3, 4, 5}?

<p>3 (D)</p> Signup and view all the answers

The range of a dataset is calculated as

<p>Highest value - Lowest value (A)</p> Signup and view all the answers

The null hypothesis is usually a statement of:

<p>No effect or no difference (A)</p> Signup and view all the answers

Which test is used to compare the means of two independent groups?

<p>t-test (A)</p> Signup and view all the answers

What does a p-value represent?

<p>The likelihood of observing the data if the null hypothesis is true (A)</p> Signup and view all the answers

What is the critical value in hypothesis testing?

<p>The threshold to decide significance (C)</p> Signup and view all the answers

The measure of how two variables move together is called

<p>Correlation (C)</p> Signup and view all the answers

The slope in a simple linear regression represents

<p>The rate of change in the dependent variable per unit change in the independent variable (C)</p> Signup and view all the answers

Which statistic indicates the strength and direction of a linear relationship?

<p>r (correlation coefficient) (D)</p> Signup and view all the answers

What is the value of r if there is no correlation?

<p>0 (B)</p> Signup and view all the answers

In multiple regression, the dependent variable is predicted based on

<p>Multiple independent variables (A)</p> Signup and view all the answers

A box plot is used to show

<p>Measures of central tendency and spread (A)</p> Signup and view all the answers

Which chart is best for categorical data?

<p>Bar chart (A)</p> Signup and view all the answers

Outliers are best identified using

<p>Box plots (B)</p> Signup and view all the answers

What type of chart is used to display parts of a whole?

<p>Pie chart (C)</p> Signup and view all the answers

A company wants to test whether three different training programs produce different levels of employee productivity. Which statistical test should they use?

<p>Chi-square test (A)</p> Signup and view all the answers

A researcher conducts a study to compare the average test scores of students in three different teaching methods. What is the null hypothesis for ANOVA?

<p>All group means are equal. (D)</p> Signup and view all the answers

If the F-ratio in an ANOVA test is large and the p-value is less than 0.05, what conclusion can be made?

<p>Reject the null hypothesis; at least one group mean is different. (C)</p> Signup and view all the answers

Which post-hoc test is commonly used after a significant ANOVA result to determine which groups differ?

<p>Tukey's HSD (B)</p> Signup and view all the answers

In a one-way ANOVA, how many independent variables are analyzed?

<p>1 (A)</p> Signup and view all the answers

A professor compares the test scores of students from three campuses. ANOVA shows ( F(2, 87) = 5.23, p = 0.003 ). What does this mean?

<p>At least one campus has significantly different test scores. (C)</p> Signup and view all the answers

What assumption must be met to conduct an ANOVA?

<p>Groups have equal variances and are normally distributed. (C)</p> Signup and view all the answers

In a study comparing satisfaction levels among four customer service methods, the ANOVA test yields ( p = 0.08 ). What is the conclusion?

<p>Fail to reject the null hypothesis; there is no significant difference. (B)</p> Signup and view all the answers

How does a two-way ANOVA differ from a one-way ANOVA?

<p>It examines the interaction effect between two independent variables. (D)</p> Signup and view all the answers

A researcher wants to compare blood pressure levels before and after using three types of medication. What type of ANOVA should they use?

<p>Repeated measures ANOVA (B)</p> Signup and view all the answers

A teacher wants to compare the mean test scores of two groups of students. Which test is appropriate?

<p>T-test (B)</p> Signup and view all the answers

What is the main difference between an independent t-test and a paired t-test?

<p>Independent t-test compares two unrelated groups, while paired t-test compares matched data. (D)</p> Signup and view all the answers

A researcher measures the effect of a new diet by comparing the weights of participants before and after the intervention. What statistical test should they use?

<p>Paired t-test (B)</p> Signup and view all the answers

The p-value in a t-test is 0.045. If the significance level is 0.05, what should the researcher conclude?

<p>Reject the null hypothesis. (B)</p> Signup and view all the answers

In a two-sample t-test, the null hypothesis states

<p>The two population means are equal. (A)</p> Signup and view all the answers

Which assumption is not required for a t-test?

<p>Equal sample sizes (D)</p> Signup and view all the answers

A researcher uses an independent t-test to compare test scores between males and females. The test yields ( t(48) = 2.02, p = 0.05 ). What does this indicate?

<p>There is a significant difference at the 0.05 level. (C)</p> Signup and view all the answers

The calculated t-value is larger than the critical t-value. What does this indicate?

<p>Reject the null hypothesis. (B)</p> Signup and view all the answers

What type of t-test is used to compare a sample mean with a known population mean?

<p>One-sample t-test (C)</p> Signup and view all the answers

A z-test is appropriate when the sample size is

<p>Greater than or equal to 30 (C)</p> Signup and view all the answers

The primary difference between a z-test and a t-test is

<p>The z-test is used when population standard deviation is known. (B)</p> Signup and view all the answers

A z-test is used to compare

<p>A sample mean with a population mean (B)</p> Signup and view all the answers

If a z-test produces ( z = 1.96 ) at ( \alpha = 0.05 ), what conclusion can be made?

<p>Fail to reject the null hypothesis. (D)</p> Signup and view all the answers

A researcher uses a z-test for proportions and gets ( p = 0.001 ). What does this mean?

<p>The result is statistically significant. (B)</p> Signup and view all the answers

What is the z-score for a value of 85, if the population mean is 70 and the standard deviation is 10?

<p>1.5 (A)</p> Signup and view all the answers

A researcher uses a z-test for a sample size of 100 and calculates ( z = 3.2 ). What does this suggest?

<p>The sample mean is significantly different from the population mean. (A)</p> Signup and view all the answers

What is the critical z-value for a two-tailed test at ( \alpha = 0.05 )?

<p>±1.96 (A)</p> Signup and view all the answers

In a z-test, if the calculated z-value is less than the critical z-value, you should

<p>Fail to reject the null hypothesis. (B)</p> Signup and view all the answers

Flashcards

Median

The middle value in a sorted dataset. If the dataset has an even number of values, the median is the average of the two middle values.

Categorical Variable

A variable that can be categorized into groups or labels, typically without a natural order.

Negative Correlation

When two variables move in opposite directions. As one variable increases, the other decreases.

Regression Equation

A mathematical equation that describes the relationship between two or more variables. It can be used to predict the value of one variable based on the value of another.

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Range

The difference between the highest and lowest values in a dataset.

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Strong Linear Relationship

When two variables have a close relationship, and their relationship can be represented by a straight line.

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Scatter Plot

A graph used to visualize the relationship between two variables. Each point on the plot represents a pair of values.

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Mode

The value that appears most frequently in a dataset.

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Descriptive Statistics

A branch of statistics that deals with the organization, summarization, and presentation of data.

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Inferential Statistics

A branch of statistics that deals with making inferences or drawing conclusions about a population based on sample data.

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Continuous Variable

A variable that can take on any value within a range.

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Correlation Coefficient

A measure of the strength and direction of the linear relationship between two variables.

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Positive Correlation

When two variables move in the same direction. As one variable increases, the other increases.

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Residual Plot

A graph that shows the difference between the predicted values and the actual values of a variable.

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Regression Analysis

A statistical technique used to model the relationship between a dependent variable and one or more independent variables.

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Kurtosis

A measure of the peakedness or flatness of a distribution.

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Skewness

A measure of the asymmetry of a distribution.

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Measures of Dispersion

Statistics that describe the spread or variability of data points around the central tendency.

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Mean Deviation

The average of the absolute deviations of each data point from the mean.

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Variance

The average of the squared deviations from the mean.

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Standard Deviation

The square root of the variance. It measures the spread of data points around the mean.

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Positively Skewed Distribution

A distribution where the tail is longer on the right side. The mean is greater than the median.

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Symmetrical Distribution

A distribution where the left and right sides are mirror images of each other.

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Normal Distribution

A symmetrical bell-shaped distribution that is common in statistical analysis.

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Probability

The likelihood of an event occurring.

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Central Limit Theorem

A statistical theorem that states that the distribution of sample means approaches a normal distribution as the sample size increases.

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Population Parameter

A numerical value that describes a characteristic of a population.

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Sampling

The process of selecting a subset of individuals from a population.

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Null Hypothesis

A statement that there is no effect or no difference between groups.

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P-value

The probability of observing the data if the null hypothesis is true.

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t-test

A statistical test used to compare the means of two groups.

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Correlation

A statistical measure that describes the relationship between two variables.

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What is a sample?

A subset of individuals selected from a larger population to represent the characteristics of the entire population.

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What is a population?

The entire group of individuals that we are interested in studying.

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What is a variable?

A characteristic or attribute that can vary among individuals in a sample or population.

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What is data?

Information collected about variables in a sample or population.

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What is descriptive statistics?

Branch of statistics that focuses on summarizing and organizing data.

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What is inferential statistics?

Branch of statistics used to draw conclusions about a population based on sample data.

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What is a distribution?

A description of the frequency of different values in a dataset.

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What is a mean?

The average of a set of values.

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What is a median?

The middle value in a sorted dataset.

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What is a mode?

The value that appears most frequently in a dataset.

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What is range?

The difference between the highest and lowest values in a dataset.

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What is variance?

A measure of how spread out the data is around the mean.

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What is a hypothesis?

A testable statement that proposes a relationship between variables.

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Study Notes

Statistics Sample Final Exam

  • Question 1: Find the median of call received in 7 days (11, 13, 17, 13, 23, 25, 19) - Answer: 17
  • Question 2: Identify the non-categorical variable - Answer: Age of a person
  • Question 3: Describe correlation if values move in opposite directions - Answer: Negative correlation
  • Question 4: Interpret regression equation (I = 50,000 - 8X) relating sales and price - Answer: An increase of $1 in price is associated with an $8,000 decrease in sales.
  • Question 5: Calculate the range of data (7, 47, 8, 42, 47, 95, 42, 96, 2)- Answer: 94
  • Question 6: Explain the meaning of a correlation coefficient close to one - Answer: Strong linear relationship between two variables.
  • Question 7: Which plot shows linear relationship between dependent and independent variables? - Answer: Scatter plot
  • Question 8: Calculate the mode and median for 7, 12, 8, 14, 21, 23, 27, 7, 11- Answer: Mode = 7, Median = 12
  • Question 9: Name a branch of statistics - Answer: Descriptive statistics
  • Question 10: Identify variables calculated by weight, height, length - Answer: Continuous variables
  • Question 11: State the use of correlation coefficient - Answer: To determine the strength of the relationship between variables x and y
  • Question 12: Describe the slope of a regression line if correlation coefficient is positive - Answer: Can be either positive or negative.

Residual plots, Correlations, and Distributions

  • Question 13: Describe the content of a residual plot - Answer: Displays explanatory variable versus residuals of the response variable
  • Question 14: Define correlation if values move in the same direction - Answer: Positive correlation.
  • Question 15: Which technique helps predict between two variables? - Answer: Regression
  • Question 16: Define Kurtosis - Answer: A measure of the degree of peakedness or flatness of a distribution.
  • Question 17: Identify the meaning of hypothesis testing - Answer: A method for accepting or rejecting hypotheses in research.
  • Question 18: What is the skewness of normal distribution? - Answer: 0
  • Question 19: Define the measure of spread - Answer: Measures of dispersion.
  • Question 20: Identify the measure of dispersion using only two values - Answer: Range
  • Question 21: Calculate range for (29, 3, 143, 27, 99) - Answer: 140
  • Question 22: Name a measure of measuring squared deviations from the mean - Answer: Variance
  • Question 23: From which measure is standard deviation always calculated? - Answer: Mean
  • Question 24: Where do the extreme values in a positively skewed distribution lie? - Answer: In the right tail
  • Question 25: Describe the distribution shape if correlation and median are identified- Answer: Symmetrical distribution

Additional Statistical Concepts and Distributions

  • Question 26: Calculate Q3 in a symmetric distribution given Q1 and Median - Answer: 40
  • Question 27: Determine the percentage of data within one standard deviation of the mean in a normal distribution. - Answer: 68%
  • Question 28: State what the area under the normal curve represents. - Answer: Probability
  • Question 29: Identify the measure of symmetry in a probability distribution. - Answer: Skewness
  • Question 30: State what a normal distribution is symmetrical around. - Answer: Mean
  • Question 31: Give the skewness for a symmetrical distribution - Answer: 0
  • Question 32: Describe the skewness of a dataset with a positive skew- Answer: Its tail extends more to the right
  • Question 33: Define the measure of kurtosis - Answer: Measures the tendency of a distribution's tails to be heavy or light
  • Question 34: State what a positive kurtosis value indicates - Answer: The distribution has heavy tails
  • Question 35: Calculate the kurtosis in a normal distribution - Answer: 3
  • Question 36: Indicate what a leptokurtic distribution represents - Answer: Heavy-tailed distribution.
  • Question 37: Calculate the probability of an event that is certain to occur - Answer: 1
  • Question 38: Describe the main result of Central Limit Theorem - Answer: The distribution of sample means approaches a normal distribution as the sample size increases
  • Question 39: State a characteristic of a normal distribution - Answer: Bell-shaped curve
  • Question 40: State the main purpose of statistics. - Answer: To summarize and analyze data.
  • Question 41: What represents a population parameter - Answer: The standard deviation of a population.
  • Question 42: What is the process of selecting a subset of individuals from a population called - Answer: Sampling

Additional Statistical Concepts

  • Question 43: What is the branch of statistics concerned with drawing conclusions from data - Answer: Inferential statistics.
  • Question 44: Calculate the probability for an impossible event - Answer: 0
  • Question 45: Define independent events - Answer: Events that cannot occur at the same time.
  • Question 46: Calculate the sum of probabilities for all possible outcomes - Answer: 1
  • Question 47: Calculate probability of getting heads in a fair coin toss - Answer: 0.5
  • Question 48: Calculate the probability of rolling a 4 on a six-sided die. - Answer: 1/6
  • Question 49: Identify the measure of central tendency most affected by extreme values. - Answer: Mean
  • Question 50: Identify the measure for spread of data - Answer: Standard deviation
  • Question 51: Calculate the mode for {2, 3, 3, 4, 5} - Answer: 3
  • Question 52: Identify the calculation for range - Answer: Highest value minus the lowest value
  • Question 53: Describe the null hypothesis - Answer: A statement of no effect or no difference.
  • Question 54: Identify a test for comparing two independent groups (means) - Answer: T-test
  • Question 55: Describe the p-value in hypothesis testing - Answer: The probability of observing the data if the null hypothesis is true.
  • Question 56: Describe critical value in hypothesis testing - Answer: The threshold for significance
  • Question 57: Identify the measure of how two variables move together - Answer: Correlation
  • Question 58: Describe the meaning of the slope in a simple linear regression - Answer: The rate of change in the dependent variable per unit change in the independent variable
  • Question 59: What statistic shows strength and direction of a linear relationship? - Answer: Correlation coefficient (r)
  • Question 60: What's the r-value for no correlation? - Answer: 0
  • Question 61: Indicate the predictor variable in multiple regression - Answer: Multiple independent variables
  • Question 62: State what a box plot displays - Answer: Measures of central tendency and spread
  • Question 63: Appropriate chart for categorical data - Answer: Bar chart
  • Question 64: State how outliers are identified using a plot - Answer: Using Box plots
  • Question 65: Identify what a pie chart displays - Answer: Parts of a whole

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Statistics Sample Final Exam PDF
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Prepare for your statistics exam with this sample final exam. Test your knowledge on key concepts such as median, correlation, and regression. Each question challenges you to apply statistics principles to real-world scenarios.

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