Statistics Final Exam Study Guide

Questions and Answers

What is the value of (d)?

0.25

0.15

0.20 (correct)

0.35

What is the probability that a randomly selected Massachusetts high school basketball player wears Adidas or Reebok sneakers?

0.0225

0.065

0.420 (correct)

0.580

What is the probability that you lose the next two matches if you have a probability of 0.6 of winning each match?

0.80

0.16 (correct)

0.40

0.36

If P(A)=0.24 and P(B)=0.52 and A and B are mutually exclusive, what is P(A or B)?

0.76 Signup and view all the answers

Which of the following is a valid assignment of digits to represent coffee drinkers in a simulation?

0,1,2,3,4,5,6= coffee drinker; 7,8,9= not a coffee drinker Signup and view all the answers

Two events are said to be mutually exclusive if:

They do not contain any outcomes in common Signup and view all the answers

Which of the following best describes the types of variables that are being measured?

Three categorical variables and two quantitative variables Signup and view all the answers

The overall shape of this distribution is:

Skewed to the left Signup and view all the answers

The mean of the distribution (don't try to find it) is:

Clearly less than the median Signup and view all the answers

Based on the shape of this distribution, what numerical measures would best describe it?

The median and the IQR Signup and view all the answers

The number of students whose favorite subject is math is:

78 Signup and view all the answers

Which of the following is the best interpretation of a z-score of -1.35 for Steve's salary?

Steve's salary is 1.35 standard deviations below the mean salary of all managers with his experience level. Signup and view all the answers

Which of the following are resistant to outliers?

The median and the IQR Signup and view all the answers

Which of the distributions below has the larger standard deviation?

Distribution A Signup and view all the answers

About how many students had scores above 39?

312 Signup and view all the answers

The median grade is in which of the following intervals?

71-80 Signup and view all the answers

This tells us that taller than average fathers tend to have taller than average sons.

True Signup and view all the answers

If sons' heights were instead measured in inches, what would happen to the correlation?

Unchanged; equal to 0.89 Signup and view all the answers

You would draw a segmented bar graph to:

Determine if gender and favorite toy as a child are associated. Signup and view all the answers

Does a positive correlation between the number of laptops and average life expectancy indicate causation?

No, the positive correlation shows richer countries have both more laptops and higher life expectancies. We don't know if there is causation. Signup and view all the answers

Which statement must be true about the individual represented by the indicated point in a residual plot?

The actual value of the response variable is smaller than its predicted value. Signup and view all the answers

The correlation between male and female illiteracy rates is r=0.945. What does this tell us?

Countries with high male illiteracy tend to also have high female illiteracy, and the relationship is very strong. Signup and view all the answers

Which variable would you put on the horizontal axis of a scatterplot in a study of TV hours and reading scores?

Hours of television, because it is the explanatory variable. Signup and view all the answers

If point (20, 25) is removed from a dataset, which statement is TRUE?

The slope will decrease and the y-intercept will increase. Signup and view all the answers

Which statement about the regression line is true?

The least square regression line has a slope of zero. Signup and view all the answers

What is the purpose of random assignment of treatments to subjects in an experiment?

To create roughly equivalent groups before treatments are administered. Signup and view all the answers

A random number generator selects 12 students from a large statistics class. The 12 students selected are:

A simple random sample of the class Signup and view all the answers

The population for this sample survey appears to be:

All adult residents of the U.S. Signup and view all the answers

This means that we expect that between 51% and 55% of all adult Americans think we should have a third party.

We expect that between 51% and 55% of all adult Americans think we should have a third party. Signup and view all the answers

Describe how nonresponse might lead to bias in this study.

A nonresponse might lead to a bias in the study because the counselor may assume that those who did not reply might have tried alcohol and they wouldn't want to tell the counselor. Signup and view all the answers

Describe how response bias might lead to bias in this study.

The counselor would have a negative bias towards those who said they have tried alcohol. Signup and view all the answers

What is the probability he will make the next free throw?

0.89 Signup and view all the answers

If quizzes are given independently of the day, what is the probability there will be a surprise quiz on the next two consecutive days?

0.09 Signup and view all the answers

Which of the following statements is false?

A probability can be a number greater than 1. Signup and view all the answers

What is the probability a randomly selected voter is affiliated with some other party?

0.05 Signup and view all the answers

What is the probability a randomly selected customer buys 3 raffle tickets?

0.25 Signup and view all the answers

Study Notes

General Statistics Concepts

Variables can be classified as categorical or quantitative; example survey measures age, gender, address duration, favorite subject, and college plans.
Distribution shapes: left-skewed indicates a longer tail on the left; mean can be less than or greater than the median based on skewness.
The five-number summary (min, Q1, median, Q3, max) provides insights into data distribution and is useful for box plots.

Measures of Central Tendency & Spread

Median and Interquartile Range (IQR) are resistant measures of central tendency and spread, not affected by outliers unlike mean and standard deviation.
Understanding correlation coefficients: r = 0.89 implies a strong positive relationship between two variables, as observed in height data between fathers and sons.

Graphical Representations

Segmented bar graphs can explore associations between categorical variables, such as gender and favorite childhood toys.
Scatterplots are effective in visualizing relationships between two continuous variables; least squares regression lines depict best-fit for prediction.

Sampling & Experiments

Random assignment in experiments aims for equivalent treatment groups, reducing bias.
Random samples yield unbiased insights about larger populations, while nonresponse can skew results if non-respondents share similar traits.

Statistics in Surveys

Population in survey context refers to the entire group represented; for instance, the survey of U.S. adults assessing political opinions.
Margins of error provide a range within which the true population parameter lies, indicating some uncertainty in survey findings.

Probability Concepts

Probability calculations for independent events, such as quizzes occurring over multiple days, involve multiplying probabilities together.
Understanding mutual exclusivity is crucial in probability; events cannot occur simultaneously.

Confounding Variables & Bias

Confounding variables can complicate causal interpretations; for example, night light usage and myopia in children suggest a relationship influenced by genetic factors.
Response bias occurs when participants' answers reflect perceived expectations rather than true opinions, impacting result validity.

Experimental Design

Double-blinding in experiments occurs when neither subjects nor experimenters know treatment allocations, minimizing bias in result interpretation.
Placebo groups are essential to understand treatment effects compared to no treatment, ensuring ethical considerations are met.

Calculating Outcomes

Familiarity with basic probability models, such as raffle ticket purchasing or sneaker brand popularity, enables clear interpretation of statistical information.
Conditional probabilities and total probabilities can guide predictions about demographic behaviors, like coffee consumption rates.

Advanced Topics

Correlation does not imply causation; statistical associations should not be misinterpreted as direct relationships.
Understanding inference from sample data to make generalizations about populations is a core aspect of statistics, requiring careful consideration of sampling methods and potential biases.

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Description

Prepare for your Statistics final exam with this study guide featuring flashcards. Each card includes important concepts, definitions, and examples that will help reinforce your understanding of variables and data types used in statistical analysis.