1 / 13

Ch 9 – Testing a Claim

9.1 – The Basics. Ch 9 – Testing a Claim. Jack’s a candidate for mayor against 1 other person, so he must gain at least 50% of the votes. Based on a poll of voters just before the election, can Jack be confident of victory?. 1. 3. 2. Random Selection of a chip. White chip = Voting for Jack.

albany
Download Presentation

Ch 9 – Testing a Claim

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. 9.1 – The Basics Ch 9 – Testing a Claim

  2. Jack’s a candidate for mayor against 1 other person, so he must gain at least 50% of the votes. Based on a poll of voters just before the election, can Jack be confident of victory? 1 3 2 Random Selection of a chip. White chip = Voting for Jack Keep drawing until your confident Jack will win Construct Scatter plot: X-axis = # of chips Y-axis = proportion of white We will do this again with a different bag with a different proportion of white chips.

  3. Two important Aspect of Hypothesis Testing: 1. increasing n help us to be more confident that there is a difference between what is observed and what is claimed. 2. It is easier to reject what is claimed if the true parameter is farther away from what is hypothesized

  4. Confidence Intervals - Estimate a population parameter Significance Test - Assess the evidence provided by data about some claim concerning a population Goal of the Two Inferences

  5. Should Jack be confident in a victory? Reasons: In reality less than 50% favor Jack, and the sample result was just do to sampling variability. If this is true, then Jack shouldn’t be confident of a victory. The sample is above 50% because more than 50% will actually vote for Jack. Then he should believe this sample and be confident of victory ONLY IF he can rule out the first reason! Suppose a random sample of 100 voters shows that 56 will vote for Jack. Is his confidence warranted? Maybe so, but there are two explanations of why the majority of voters in the sample seem to favor Jack.

  6. A Fathom Simulation was done to simulate 400 samples of size 100 from the population in which exactly 50% of the voters support Jack. 55 of the 400 trials had a sample proportion of 56% or higher. Jack should be worried of winning! 13.75% is a high chance that these results would have happened by pure chance alone if the true value is 50%. It is plausible that 50% of the voters do not favor Jack.

  7. Stating our Hypotheses Null Hypothesis – H0 : this is the claim we are testing. This is typically a statement of no difference. H0: (parameter symbol) = ## Alternate Hypothesis – Ha : this is the claim about the population that we are trying to find evidence for This statement is one-sided or two-sided. Ha: (parameter symbol) > ## Ha: (parameter symbol) < ## Ha: (parameter symbol) = ##

  8. ALWAYS STATE THE HYPOTHESIS BEFORE USING THE DATA!!!!HYPOTHESES ARE ABOUT A POPULATION.YOUR EVIDENCE IS YOUR SAMPLE.

  9. P-VALUE • Assuming the Ho is true, the probability the p-hat of x-bar would take on a value more extreme than the 1 observed • Smaller = the more rare our sample results are and the more evidence we have to support Ha and against Ho • Larger = the more likely our sample results our and the less evidence we have to support Ha and we fail to reject Ho.

  10. Interpret the P-value for Jack’s chances of winning • If exactly 50% support Jack, there is a 13.75% chance in a sample of 100, 56% or more would actually support him by random chance alone. • Since this is not a rare occurrence, Jack should be worried that 50% actually support him.

  11. Mike tries a new 7-iron. He has years of experience and knows his mean is 175 yards and his standard deviation is 15 yards using his old club. He hope this new club will make him more consistent. Describe the parameter of interest. State the hypotheses for performing a significance test.

  12. From 50 shots, his sample standard deviation is 10.9 yards. A significance test was performed and the p-value is 0.002 Interpret the P-value. Does the data provide convincing evidence against Ho? Explain

  13. How low is low? • Statistically Significant level – alpha • Stated BEFORE the test is conducted. • Typically 0.05 (or 0.01) it depends on the context and severity of the results.

More Related