Download A Review of Hypothesis Testing (Chapters 6-8)

Exam 2 Review
Confidence intervals (chapters 6, 7, and 8):
 estimate  margin of error
 help us to come up with the most plausible estimate(or range) for our population parameter
 confidence means: in the long run, 95% of the confidence intervals we make will cover the true unknown
parameter
 no guarantee that OUR particular interval will cover the parameter, it is random
 margin of error can be reduced by:
o larger sample size (usually)
o smaller confidence level (not desired)
 need a simple random sample (SRS) from a normal population
 the bigger the sample size, the better job the confidence interval will do of predicting the true parameter,
interval gets narrower
 outliers are bad news
 margin of error covers only random sampling errors (errors due to chance)
 bad data gives bad confidence intervals
Hypothesis testing (chapters 6, 7, 8, and 9):
 Know how to construct hypothesis for the different chapters
 H0 always gets the = sign, except in chapter 9
 Hypotheses always refer to the population parameter, never the sample
 The P-value is the probability that you would get a result as extreme or more as your sample result,
assuming H0 is true
 If that P-value is small (less than α) then we reject H0 because we don’t think it is very likely that H0 could
be true (given the data at hand)
 P-values are ALWAYS between 0 and 1 because they are probabilities
 You can never prove either hypothesis true, we only provide evidence for the alternative or NOT enough
evidence for the alternative
 Reject/do not reject H0 but never accept anything!
 Use the P-value to draw a conclusion, be able to write the conclusion in plain language
o Reject H0: My data provides evidence for … (the alternative)
o Fail to Reject H0: My data does not provide enough evidence for … (the alternative)
 Always restate your conclusion in terms of the original story, using the wording from the stated problem.
 Know how to use Confidence Intervals to draw a conclusion for an appropriate 2-sided test
o Ha can only be , Confidence = 1 – 
 If the P-value   (the significance level), then you reject H0
 If you reject H0, the results are statistically significant
 The smaller the P-value, the stronger our evidence for rejecting H0
 P-value is the amount of evidence we have. Smaller P-value = more evidence
 A larger sample size can increase your chances of being able to reject H0
Other things:
 Calculating sample sizes for a give margin of error (for both means and proportions)
 Reading all tables to get critical values and P-values
 Know when to use which formula/situation
 Use and abuse of Significance Tests
 Robustness of t-procedures, when do they work in real practice?
 Relative Risk, calculating and interpreting
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Chapter 6 (Means)
 One-sample Mean
 We know , the population standard deviation
 Use Z, the normal distribution for test statistics and confidence intervals
 A 1-sided hypothesis test might look like: H0 :   3
Ha :   3
Chapter 7 (Means)
 We do not know , the population standard deviation
 We usually need to calculate s, the sample standard deviation
 Use the t distribution for test statistics and confidence intervals (need degrees of freedom)
 One-sample Means
 Only one set of data
 A 1-sided hypothesis test might look like: H0 :   3
Ha :   3
 Matched Pairs for Means
 Before/after or left/right situation. You have 2 scores from the same units or subjects.
 A 1-sided hypothesis test might look like: H0 : diff  0
Ha : diff  0 , where diff  after  before
 Two-sample Comparison of Means
 Comparing means for two separate samples (men vs. women OR freshmen vs. seniors, etc)
 A 1-sided hypothesis test might look like: H0 : men  women  0
Ha : men  women  0
Chapter 8 (Proportions)
 Know either the sample proportion p̂ or X = the # of successes and also know n = the sample size
 Use Z, the normal distribution for confidence intervals and test statistics
 Proportions are always between 0 and 1
 1-sample proportion
 Only one set of data
 A 1-sided hypothesis test might look like: H0 : p  0.7
Ha : p  0.7
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2-sample comparison of proportions
 Comparing proportions for two separate samples (men vs. women, for example)
 A 1-sided hypothesis test might look like: H0 : pmen  pwomen  0
Ha : pmen  pwomen  0
Chapter 9 (Two-way Tables)
 Two categorical variables
 Write out the hypothesis with words, no parameters:
H0 : There is no association between eye color and hair color.
Ha : There is an association between eye color and hair color.
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Use  (chi-squared) distribution. SAS output gives test statistic, P-value, and degrees of freedom.
Know the rules for when it is ok to do this test
Joint, marginal, and conditional distributions can be calculated and/or read from SAS output
Often like to make bar graphs of marginal and conditional distributions
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