1 / 17

Fundamentals of Hypothesis Testing

Fundamentals of Hypothesis Testing. Chapter 10 Created by Laura Ralston. Outline. 10.1 Fundamentals of Hypothesis Testing 10.2 Hypothesis Testing for Means (Small Samples) 10.3 Hypothesis Testing for Means (Large Samples) 10.4 Hypothesis Testing for Population Proportions ?

doane
Download Presentation

Fundamentals of Hypothesis Testing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Fundamentals of Hypothesis Testing Chapter 10 Created by Laura Ralston

  2. Outline • 10.1 Fundamentals of Hypothesis Testing • 10.2 Hypothesis Testing for Means (Small Samples) • 10.3 Hypothesis Testing for Means (Large Samples) • 10.4 Hypothesis Testing for Population Proportions ? • 10.5 Types of Errors • 10.6 Hypothesis Testing for Population Variance • 10.7 Chi-Square Test for Goodness of Fit • 10.8 Chi-Square Test for Association

  3. Introduction • Anyone can make a claim about a population parameter • “Four out of five dentists prefer StarBrite toothpaste” • “Fewer than 1% of dogs attack people unprovoked” • “In any given one-year period, ….about 18.8 million American adults suffers from a depressive illness” –Reader’s Digest • “For cars, this Corporate Average Fuel Economy has been 27.5 miles per gallon since 1990….” USA Today

  4. People make decisions everyday based on such claims. • Some decisions are insignificant (which toothpaste to buy) • Others are very important! • Whether to use a new prescription drug that has just come onto the market • Purchase a car based on reported safety ratings • Are public safety campaigns working? • Which candidate is likely to win an election?

  5. Hypothesis Testing • One statistical process that sets a uniform standard for evaluating claims about a population parameter • Foundation for hypothesis testing is the RARE EVENT RULE: if, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct (Gender selection example from Triola)

  6. Step 1: State the hypotheses in mathematical terms Null Hypothesis, H0 Alternative Hypothesis, H1 or Ha Claim about a population parameter Opposite of the null hypothesis • Claim about a population parameter • Always contains “equals” Indicate which hypothesis is stated in the given problem (o.c.). This information is needed later.

  7. Common Phrases

  8. Step 2: Determine the critical value(s) • Based on the level of significance, a, which will be given in the problem and using normal distribution • Critical value(s) separates “guilty” and “not guilty” • Use calculator: invNorm command • “Type” of test is determined by Ha which will determine the critical region(s) and ultimately the critical value(s) • Right-Tailed test if > or > (picture) • Left-Tailed test if < or < (picture) • Two-tailed test if ≠ (picture, a/2)

  9. Step 3: Calculate test statistic • Test statistic will vary depending on the parameter and sample size (z, t, or chi-square) • Used to make a decision about the null hypothesis, “evidence” • Calculated using sample data (given in problem)

  10. Step 4: Make a decision • Variety of methods (traditional, p-value, confidence intervals) • Two possibilities • Reject the Null Hypothesis -assumption is not valid based on this set of sample data • Fail to reject the Null Hypothesis (never “accept”)-assumption is valid based on this set of sample data

  11. Step 5: State final conclusion in non-technical terms • Conclusion should be well-worded, reference the original claim, and free of mathematical symbols. • See flow chart on next slide to help determine wording

  12. Yes YES (original claim contains equality) No Yes NO (original claim does not contain equality) No

  13. Example 1 • In a sample of 27 blue M&Ms with a mean weight of 0.8560 g. Assume that s is known to be 0.0565 g. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean weight of all M&Ms is equal to 0.8535 g (the weight necessary so that bags of M&Ms have the weight printed on the packages).

  14. Example 2 • In a sample of 106 body temperatures with a mean of 98.20°F. Assume that s is known to be 0.62°F. Consider a hypothesis test that uses a 0.05 significance level to test the claim that the mean body temperature of the population is less than 98.6°F.

  15. Example 3 • The average production of peanuts in the state of Virginia is 3000 pounds per acre. A new plant food has been developed and is tested on 60 individual plots of land. The mean yield with the new plant food is 3120 pounds of peanuts per acre with a standard deviation of 578 pounds. At a 0.05 significance level, can one conclude that the average production has increased?

  16. Example 4 • A researcher claims that the yearly consumption of soft drinks per person is 52 gallons. In a sample of 50 randomly selected people, the mean of the yearly consumption was 56.3 gallons. The standard deviation of the sample was 3.5 gallons. At a 0.01 significance level, is the researcher’s claim valid?

  17. Assignment • Use traditional method ---modeled in above examples • Page 498 #25-30

More Related