Elementary Statistics 201:11



Elementary Statistics 201:23

Final Review

The Exam is Friday, April 8, 9-11:30am, in the gym, even rows 2-10.

Sections of the textbook that you should be familiar with:

Chapter 1: Sections 1-7 Chapter 2: Sections 1-7 (10)

Chapter 3: Sections 1-7 Chapter 4: Sections 1-3, 5-7

Chapter 5: Sections 1-4 Chapter 6: Sections 1-5

Chapter 7: Sections 1-6 Chapter 8: Sections 1-4

Chapter 11: Sections 1,2,5

There will be a formula sheet given with the exam, it will be the last two pages of the textbook.

There will be two tables given: Standard Normal Table and Student t Table. You use the Standard Normal Table for determining information about a normal distribution, and also for finding critical values for confidence intervals and hypothesis tests of means from large samples or proportions. Use the Student t Table for confidence intervals and hypothesis tests of means from small samples (n ≤ 30).

Basic Concepts: You should be able to define in your own words, recognize, and give an example of:

Statistic, population, sample, parameter, data (quantitative vs qualitative, discrete vs continuous), sampling (stratified, systematic, random, cluster)

Frequency tables: know how to fill in, use to create relative frequency tables, histograms, probability distributions, find descriptive statistics (see below)

Measures of Centre: Mean, median, mode know what they are, how to get them from data sets, frequency tables, weighted values, probability distributions, binomial distributions, normal distributions

Measures of Variance: Standard Deviation and Variance- know what they are, how they can be used to make interpretations, how to get them from the appropriate formula (and know which formula to use), empirical rule, Chebyshev’s rule

Measures of Position: z-score (how to use formula and how to interpret- what are the usual values), how to find quartiles and percentiles- from data set, frequency table, normal distribution; know how to find a corresponding boxplot, how to determine if something is an outlier

Probability: Possible values, complement, addition rule (how to use intuitively), when are events mutually exclusive, multiplication rule (how to use intuitively), when are events conditional, how to determine if events are independent, probabilities from frequency tables or from distributions.

Distributions: Probability (what are requirements?), binomial (what are requirements?), standard normal distribution, how to convert normal to standard, how to use standard normal table to find probabilities, or to find z-score given probability, how to use the normal distribution to approximate the binomial

Central Limit Theorem: What are sampling means? What does theorem say? How do you find the population mean and standard deviation of a certain sample size?

Confidence Intervals: Know how to determine critical values for a certain confidence level. For means from a large sample and proportions, use Standard Normal Table. For means from a small sample use Student t. You should also be able to determine sample size for determining the confidence interval of a mean or a proportion.

Hypothesis Testing (one sample): For any hypothesis test, the first step is identifying the claim and its opposite. Decide which is the Null H0 and which is the Alternative Ha, the Null always contains =, ≤, or ≥. Use Ha to determine the rejection region. ≠ means two tails, < means left tail, > means right tail. (Also should know what Type I and Type II errors are). Identify what your significance level α is. To find the rejection regions: mean from large sample and proportion, use Standard Normal; mean from small sample, use Student t. The tails are the rejection region. Then find your test statistic: z for mean from large sample or proportion, t for mean from small sample. If your test statistic is in the rejection region, reject the Null, there is sufficient evidence that the Null is not true. If the test statistic is not in the rejection region, then do not reject the Null. There is not sufficient evidence that the Null is not true. Another way to do a hypothesis test is to check the p-value. After finding your test statistic, find the probability that a value is more extreme than it (so the area of the tail formed where the test stat is the cutoff). If this probability (the P-value) is less than α, then it is in the rejection region and you can reject the Null. If the test stat is a z-score, then you can use the standard table to find it. If not z, then you need stats software (and so would be given to you). Be sure to state your conclusion in terms of the original claim.

Two Samples: The hypothesis tests and confidence intervals are similar to the ones from one sample, but now look at the differences. If a claim is that two means or proportions are the same, then the claim is that their difference is 0. An inference can be about the difference between means or for paired data it can be the mean of the differences.

Correlation and Regression: For a finite sample of data points of the form (x,y). Know how to use the formula to determine correlation r. What does correlation tell you? You should know how to find the regression line (sometimes called prediction equation or least squares line) for the data, and use it to make predictions. When is the regression line useful for making predictions?

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