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Hypothesis Testing Classical Approach

Hypothesis Testing Classical Approach. Chapter - 7.1; 7.2; 7.3. Hypothesis Testing. Have you ever questioned results or statistics about a specific situation that just seem like they are inaccurate? This is a procedure that is used to check if the results of a study are true.

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Hypothesis Testing Classical Approach

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  1. Hypothesis TestingClassical Approach Chapter - 7.1; 7.2; 7.3

  2. Hypothesis Testing • Have you ever questioned results or statistics about a specific situation that just seem like they are inaccurate? • This is a procedure that is used to check if the results of a study are true. • It is a decision making process for evaluating claims made about a population. • Recall that most studies done use a sample of the population, then generalize the results to the entire population.

  3. Steps of Hypothesis Testing • Each test must begin with a conjecture which is either true or false. • Null Hypothesis – (H0 ) – is assumed true until evidence proves otherwise. There is no difference between the results and a specific value. • Alternative Hypothesis – (Ha ) – is a statement to be tested. We are trying to find evidence that shows existence of a difference between the results and a specific value.

  4. Review of important symbols:

  5. Types of TESTS(see chart p.365 & p. 370) • Two-Tailed Test – is used to make a conjecture that the data from the study is NOT equal to what is claimed. • Right-Tailed Test – is used if the alternative hypothesis contains a greater than symbol. • Left-Tailed Test – is used if the alternative hypothesis contains a less than symbol.

  6. Two-Tailed Test • Stating the Null and Alternative Hypothesis For a two-tail test – remember to split the level of significance.

  7. Two-Tailed Test (Ex 1) – Ford claims that the Escape will get 25 mpg, highway. Write the Null and Alternative Hypothesis:

  8. Symbol of Equality • When dealing with greater than or less than inequalities, they are always placed into the ALTERNATIVE hypothesis. • The NULL hypothesis must ALWAYS contain an equals sign. ( < , > ) • Thus, the claim could be part of the Alternative in some problems. • Choose the Complement of the inequality to place in the Null or Alternative Hypothesis

  9. Left-Tailed Test • Stating the Null and Alternative Hypothesis:

  10. Left-Tailed Test (Ex 2) – The mean number of hours a particular battery claims to run is at least 500 hours. State the Null and Alternative Hypothesis: (CLAIM)

  11. Left-Tailed Test (Ex 2a) – The mean number of hours a particular battery claims to run is less than 500 hours. State the Null and Alternative Hypothesis: (CLAIM)

  12. Right-Tailed Test • Stating the Null and Alternative Hypothesis:

  13. Right-Tailed Test (Ex 3) – The 1g I-Pod Nano claims it can hold at most 500 songs. State the Null and Alternative Hypothesis: (CLAIM)

  14. Right-Tailed Test Right-Tailed Test (Ex 3) – NCCC claims that the average tuition paid is more than $1000. (CLAIM)

  15. Finding Error in Testing: • Type I Error – if one rejects the null hypothesis when it is true. • Type II Error – if one does not reject the null hypothesis when it if false. • This is classically compared to a courtroom decision on guilt of a defendant. • See p. 367; assume the innocent until proven guilty.

  16. Steps to Perform a Hypothesis Test: • State the hypothesis, Null and Alternative • Specify the LoS: α = from Table IV. • Sketch a curve. Place LoS value on it. • Compute the Test Value. Place on sketch. • Make a decision to “reject” or “not reject” the null hypothesis. • Summarize the results.

  17. The Test Value • This value is found with the following data being available: • Sample size • Sample Mean • Population Mean (Claim) • Standard Deviation (given or assumed)

  18. Level of Significance • is given in each problem and is used to find the critical value. • We will be using Table IV to find the Critical Value, which is the number of S.D.’s the sample mean can be from the population mean before we reject the Null hypothesis. • The shaded region in our curve will represent the rejection region. When we will reject the null.

  19. Lets try a few problems: When doing each problem, be sure to do the following: • Follow the 6 steps. • Have Table IV handy to compute the critical region, rejection region. • Actually draw a curve to represent your hypothesis. • Compare the critical value and the test value to determine if you will be rejecting he Null. * Decision is based on REJECTION REGION.

  20. Let’s find Critical Values: • These values will define the beginning of the rejection zone. They are found in TABLE 4! • We will only split the LoS for Two-tailed Z’s Ex 1 –Level of Significance = .10; Two-tail Ex 2 – Level of Significance = .01; Right-tail Ex 3 – Level of Significance = .10; Left-tail Z = +/- 1.645 Z = +/- 2.33 Z = +/- 1.28

  21. TWO – TAILED Level of significance .10 = =/- 1.645 .05 = +/- 1.96 .01 = +/- 2.575 * each of these levels are cut in half, then found in table IV LEFT or RIGHT Level of Significance .10 = +/- 1.28 .05 = +/- 1.645 .01 = +/- 2.33 * Each of these levels can be found right away in table IV Critical values received from TABLE IV * These are the most commonly asked.

  22. Determine if you will reject based on the given LoS and Test Z: (Ex 1) Right-tailed test, Level of Significance: α = .05; Z = 1.75 (Ex 2) Left-tailed test, Level of Significance: α = .10; Z = - 1.26 (Ex 3) Two-tailed test, Level of Significance: α = .01; Z = - 2.45 Critical zone = +/-1.645, thus Do not reject Critical zone = +/-1.28, thus reject Critical zone = +/-2.33, thus Do not reject

  23. Practice without word problem: Given: μ = 25; σ = 2.1 n = 40 α = .05 • Determine the type of test. • Find the critical value of the rejection region. • Determine the Test Z-value • Decide to Reject or Not reject We will reject the null!

  24. Math SAT Scores: (Ex 4) – According to collegeboard.com, the mean score in the United States on the Math section of the SAT’s is a 520. Mr. Najuch samples 50 Math SAT scores. The mean for these 50 students is 545 and σ = 90. Does the sample provide enough evidence to reject the claim at a α = 0.1 level of significance?

  25. Answer to (Ex 4) Step 1: Step 2: Level of significance = 0.1 Step 3: Compute test value: Step 4: Make a decision, draw the curve, put critical value in, as well as test value. - we will reject the null hypothesis, because the test value is in the rejection zone Step 5: Summarize; There is sufficient evidence to reject the claim of collegeboard.com that mean score is a 520. 0.1 = +/- 1.645

  26. Smoking is BAD! (Ex 5) – According to nysquits.org, the mean age a person tries their first cigarette is at least 14 years old. The study was done in 2002. A health care provider wants challenge this claim. He obtains a random sample of 30 people that have tried smoking and finds the mean age to be 12.8 and σ = 2.1 years, does the sample provide enough evidence that people are trying younger at a α = 0.05 level of significance?

  27. Answer to (Ex 5) Step 1: Step 2: Level of significance = 0.05 Step 3: Compute test value: Step 4: Make a decision, draw the curve, put critical value in, as well as test value. - we will reject the null hypothesis, because the test value is in the rejection region, Step 5: Summarize; There is sufficient evidence to reject the claim made by nyquits.org 0.05 = +/- 1.645

  28. First home: (Ex 6) – According to mortgage.com, in the U.S., the mean age a person buys their 1st house is less than 30 years old. A realtor wants to challenge this claim. She obtains a sample of 75, 1st home buyers and gets an average age of 29 of a σ = 3.8 years, does the sample provide enough evidence that mean age is different at a α = 0.01 level of significance?

  29. Answer to (Ex 6) Step 1: Step 2: Level of significance = 0.01 Step 3: Compute test value: Step 4: Make a decision, draw the curve, put critical value in, as well as test value. - we will not reject the null hypothesis, because the test value is not in the rejection region Step 5: Summarize; There is insufficient evidence to conclude that people are buying their 1st home at a different age. .01= -2.33 Claim

  30. Small Samples (less than 30) Chapter 7.3 shows the method for working with small samples. Using Table 5 – t-dist. Degrees of freedom = n-1; where n equals the sample The steps are the same…..table and formula are different:

  31. Let’s try one: A local HS advertises it’s mean SAT score is 1150 combined Math and English. You want Challenge this. You obtain 12 scores and find an average of 1075, σ = 80. Is there enough evidence at a α = .05 level, to reject the claim?

  32. ANSWER: Two-tailed test! There is enough evidence to reject the claim.

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