- Describe in every day language what a Type I or Type II error is.
- A Type I Error is to say false when true. (Everyday)
- A Type II Error is to say true when false. (Everyday)
- A Type I Error is to reject a true null hypothesis. (Statisically)
- A Type II Error is to fail to reject a false null hypothesis. (Statisically)
- Know which distribution should be used to test (4 questions) ...

Test |
Distribution |
Notes | |

Mean(s) | Z or T | Use Z if sigma is known Use T if sigma is unknown Two samples with Dependent case creates a new variable for which you then find the sample standard deviation, so use T. | |

Proportion(s) | Z | np >= 5, nq >= 5 | |

Variance | Chi-Square | ||

Variance(s) | F | Put the larger variance on top will make it be a right tail test. |

- Know the default level of significance.
- 0.05
- Know the definition of the level of significance.
- The probability of being in the critical region
- The probability of being more extreme than the critical value
- The probability of committing a Type I Error
- The probability of rejecting a true null hypothesis
- Know the definition of the critical value.
- The value which separates the critical region from the non-critical region
- The value which separates the values which cause rejection from the values which would not cause rejection
- Know the definition of null and alternative hypotheses.
- Null: Statement of no change
- Null: Always contains the equal sign
- Alternative: Statement of change
- Alternative: Does not contain the equal sign
- Know the definition of the probability-value.
- The probability of being more extreme than the test statistic
- Know the definition of the F-variable.
- The ratio of two independent chi-square variables divided by their respective degrees of freedom.
- Know the relationship between prob-value, test statistic, level of significance, and critical values.
- The test statistic is to the critical value as the p-value is to the level of significance
- The test statistic is to the p-value as the critical value is to the level of significance
- Know the difference between the decision and conclusion as to whether the null hypothesis or original claim is used.
- The decision is based on the null hypothesis.
- The conclusion is based on the original claim.
- Know the difference between critical value and test statistic as far as which is looked up and which is calculated.
- The critical value is looked up
- The test statistic is calculated
- Know the results from the classical approach and how they differ from the results with the prob-value approach.
- The classical approach and the probability-value approach will always have the same results.
- P-value: Reject if the p-value is less than the level of significance, no matter what type of test it was.
- Classical: Depends on the type of test
- The p-value is easier for a computer to calculate
- You can decide your own level of significance if you're given a p-value without having to look up another critical value
- The end-user can look at a p-value and make a decision without having to know where the p-value came from
- Know properties of the Standard Normal distribution.
- Symmetric about its mean
- Mean is 0
- Standard deviation and variance are 1
- About 68% lies within one standard deviation of the mean.
- About 95% lies within two standard deviations of the mean.
- About 99.7% lies within three standard deviations of the mean.
- It's better suited to the p-value approach
- Know properties of the Student's T distribution
- Symmetric about its mean
- Mean is 0
- Standard deviation and variance are greater than 1
- Requires degrees of freedom
- Actually many distributions
- Approaches the normal distribution as the sample size gets larger
- Discovered by Irish Brewery worker William T. Gosset
- Better suited to the classical approach
- Know properties of the Chi-Square distribution.
- Not symmetric
- No negative values
- Requires degrees of freedom
- Actually many distributions
- To look up a critical value on the left, you must first subtract the area on the left from one and then look it up.
- Best suited to classical approach
- Mean is its degrees of freedom
- Variance is its degrees of freedom
- Know properties of the F Distribution
- Not symmetric
- No negative values
- Requires two different degrees of freedom, one for the numerator and one for the denominator
- It is the ratio of two independent chi-square variables divided by their respective degrees of freedom
- Mean is approximately 1
- Placing the larger variance on top will make it a right tailed test
- Requires several different tables, one for each level of significance
- Best suited to the classical approach
- Know which distributions are best used with the classical approach and which are best used with the prob-value approach.
- P-value approach is best suited when the critical values are given on the outside of the table and the probabilities are looked up on the inside
- Classical approach is best suited when the probabilities are given on the outside of the table and the critical values are looked up on the inside.
- P-value approach works best with a Normal distribution.
- Classical approach works best with a Student's t, Chi-Square, or F distribution
- Know when to reject the null hypothesis using both the classical and prob-value approaches.
- Prob-value: Reject if the prob-value is less than the level of significance
- Classical: Reject if the test statistic is less than the critical value for a left tail test
- Classical: Reject if the test statistic is greater than the critical value for a right tail test
- Classical: Reject if the test statistic is less than the left critical value or greater than the right critical value for a two tail test
- Classical: Reject if the test statistic is more extreme than the critical value
- Look up the critical values for a test about a single population mean.
- If you know sigma, then use Z
- If you don't know sigma, then use T and let degrees of freedom = n-1
- Use the appropriate row (one-tail or two-tail)
- Make critical value negative for a left tail test
- Give two critical values (positive and negative) for a two tail test
- Look up the critical values for a test about a single population mean.
- See previous problem.
- Look up the critical values for a test about a single population variance.
- Use chi-square table
- Degrees of freedom is n-1
- If right tail, then just look up critical value in table
- If left tail, subtract level of significance from 1, and then look up.
- If two tail, then divide the level of significance by two.
- Look up that area for the right critical value
- Subtract that area from one and look up for the left critical value
- Do NOT make negative - remember, chi-squares are non-negative
- Look up the critical values for a test about two population variances.
- Use the F-table
- Divide the level of significance by two for a two tail test
- Place the larger variance in the numerator to make it a right tail test
- Find the prob-value for a test statistic which isn't a value directly in the table. The best that you will be able to do is to say the prob-value is between two probabilities
- Go to the appropriate degrees of freedom in the table
- Find the two critical values on either side of your test statistic
- Go to the top of the table and read the two probabilities for those columns.
- The p-value will be between those two probabilities
- Use the one-tail or two-tail rows depending on the type of test.
- Do NOT make negative for a left tail test - these are probabilities, they can't be negative
- Look up the critical value in a chi-square table when the degrees of freedom aren't in the table. You should go to the value in the table which is less likely to reject in error.
- Use the critical value (inside of the table) which is more extreme
- Larger critical value for a right tail test
- Smaller critical value for a left tail test
- Do not pick the larger or smaller degrees of freedom, pick the larger or smaller critical value.
- Tell how you can tell whether the test for a single population mean is a left-tail, right-tail, or two-tail test by looking at the critical value(s).
- Negative critical value implies left tail
- Positive critical value implies right tail
- Negative and positive critical values imply two tails
- Calculate the test statistic used to test the equality of two population variances (F-test).
- F is the ratio of the variances
- Put the larger variance on top to make it a right tail test
- Be sure to square if the standard deviations are given
- A claim and level of significance are given. You are told the decision and you need to write the conclusion.
- Look at the decision
- Reject the null hypothesis means there is sufficient evidence
- Fail to reject the null hypothesis means there is insufficient evidence
- Determine if the original claim is the null or alternative hypothesis
- If the original is the null hypothesis, then there is _____ evidence to reject the claim
- If the original is the alternative hypothesis, then there is _____ evidence to support the claim.

- Problems 1 - 6 are short answer.
- Problems 7 - 15 are true false.
- Problems 16 - 21 are multiple choice
- None of the problems are directly from the text (that I know of).