Mt 120 Applied Statistics - Spring 2003

Study Guide for Final Exam

The cumulative final exam is scheduled for Thursday, May 15, 10:30 a.m. to 12:30 p.m. It will contribute 20% to your final course grade.

This test will focus on the major ideas of this course. It will include material from those portions of Chapters 1 through 10, and Chapter 12 that we have covered in lecture, class activities, reading assignments, and graded homework assignments.

You may use your text book and one 3"-by-5" note card that you have prepared ahead of time. The Supplementary Exercises at the ends of each chapter may provide me with some inspiration as I make up test questions.

I expect that you will have the use of a calculator as you work on this test. You should be able to use the calculator to add, subtract, multiply, divide, square, and take square roots. You will also be expected to use Excel for one problem during the exam.

Kinds of questions on this exam

• There will be ten short answer questions asking you to identify something or to do a short calculation. (20% of the exam)

• There will be one problem from our study of Descriptive Statistics (Chapters 1 - 3). (20% of the exam)
• There will be one problem on Probability Distributions (Chapters 4 - 6). (20% of the exam)
• There will be one problem from Inferential Statistics, Confidence Intervals, and Hypothesis Testing (Chapters 7 - 9). (20% of the exam)
• There will be one problem about the relationship between two variables -- Covariance, Correlation, and Regression (Section 3.5 and Chapter 14). (20% of the exam)
  • One of these problems will require you to enter data into an Excel worksheet, and use the features of Excel to help you solve the problem.

Use of Excel

You should be able to

Enter data into an Excel worksheet

Use Excel to calculate basic descriptive statistics (e.g., the mean, median, mode, variance, standard deviation)

Use Excel to calculate a relative frequency table

Use Excel to create an appropriate chart to display the data

Use Excel to compute binomial, Poisson, and normal probabilities

Use Excel to calculate a confidence interval using either the normal or the t distribution (whichever is appropriate for the given situation)

Use Excel to calculate covariance between two variables a correlation coefficient for two variables, and draw a regression line

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Descriptive Statistics (Chapters 1 - 3)

You should be able to organize and summarize a given set of data with up to 20 data values.

Construct a stem-and-leaf display

Calculate the median, the first and third quartiles

Calculate the mean, the median, and the mode

Calculate the range, and the interquartile range (IQR)

Use the variance or the standard deviation to estimate a 68%-confidence interval for the population mean

Give a 5-number summary for a given data set

Calculate measures of relative location -- that is, calculate z-scores

Identify any outliers in the data set, or explain how you know that there are no outliers

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Probability Distributions (Chpater 4 - 6)

You should be able to work with various probability distributions.

Determine whether a given function is a valid probability function (Does it meet the two conditions for being a probability function?)

Evaluate probabilities for situations which follow a given discrete probability distribution (This involves evaluating the probability function at particular values.)

Recognize a situation which follows a continuous probability distribution and set up a probability function for this situation

• Evaluate probabilities for situations which follow a continuous probability distribution (This involves calculating areas over a range of values.)

Calculate the expected value for a discrete random variable using its probability function

Recognize a situation which follows a uniform distribution and set up a probability function for this situation

Recognize whether the problem situation uses a discrete uniform, binomial, Poisson, continuous uniform, or normal distribution --- and identify characteristics of the problem situation that determine which probability distribution is the best model for the situation

Recognize a situation which follows a binomial distribution and set up a probability function for this situation

• Use a tree diagram to illustrate various possible outcomes for a binomial experiment
• Determine values for n and p for a problem situation involving a binomial experiment,
• Use your calculator to evaluate the binomial probability function for a particular value of x (assuming that you have determined n and p for the binomial experiment)

Recognize a situation which follows a Poisson distribution and set up a probability function for this situation

• Apply what you learned in doing graded homework 4 to recognize a problem situation as Poisson experiment
• Determine the value for mu for a problem situation involving a Poisson experiment
• Use your calculator to evaluate the Poisson probability function for a particular value of x (assuming that you have determined mu for the Poisson experiment)

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Inferential Statistics, Confidence Intervals, and Hypothesis Testing (Chapters 7 - 9)

For a given problem scenario, you should be able to

Give a point estimate for the mean of a population by using the mean of a sample

Use the Empirical Rule to estimate the proportion of a population that is within one, two, or three standard deviations of the mean

Explain the significance of the Central Limit Theorem in setting up a confidence interval for the mean when you are taking samples from a given population

Recognize whether the problem situation is talking about individual data values, or involves the mean of a sample of size n

Convert given data values to z-scores

Use the standard normal table to calculate probabilities for particular events which follow a normal distribution

Calculate a confidence interval for the population mean with a given level of confidence from a large or small sample taken from that population

Determine the appropriate sample size that would be needed to get a confidence interval with a given margin of error

Develop appropriate null and alternative hypotheses for the question or problem that is being studied

Comment on the consequences of rejecting or not rejecting the null hypothesis

• Identify the Type I error for the situation, and the consequences of making this type of error
• Identify the Type II error for the situation, and the consequences of making this type of error

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Correlation and Regression (Section 3.5 and Chapter 14)

For a given problem scenario, you should be able to

• Construct a scatter plot of the data
• Draw a line through the data which seems to represent the trend of the data
• Estimate the slope and the y-intercept of this line (or get Excel to calculate these for you)
• Use Excel to calculate the covariance and the correlation for the given data
• Interpret what the covariance and the correlation coefficient tell you about the strength of the relationship in the data