The hypothesis process 2
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Just a Slide explaining the process. Hope it helps.
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The hypothesis process 2
- 1. The Hypothesis Process EXPLAINING THE HYPOTHESIS TEST PROCESS PRESENTED BY TEAM A: ROGER GOMEZ, CHRISTIAN GLORIA, AND DUSTIN BUJANDA
- 2. The Problem The claim by a weight loss company is that, on average, the client will lose 10 pounds over the first two weeks. 50 people who joined the program were sampled. Their weight loss is 9 pounds with a standard deviation of 2.8 pounds. Can we conclude, at the .05 level (95% confident), that a person will lose less than 10 pounds.
- 3. List Important Data 𝜇 = Mean from Claim, Prediction, Null Hypothesis 𝑥 = Sample Mean (Actual findings from study, research, analysis. 𝛼 = Level of Significance (.05, .01, .10); 𝛼/2 S = Standard Deviation (Find the Variance, take the ) ∩ = Sample size, # of Observations
- 4. Draw “Comparison Distribution” 10 0 0.05 95% Cutoff Z-score = -1.65Z-Table .05/1= .05
- 5. Calculate or Pick a Critical Value 1. Level of Significance Chosen by Researcher or Client. 2. Most Common Are: .05 (95% Confident), .01, .10 3. The Formula for Critical Value is: Zα/2 4. Will appear in problem as … a. Can we conclude, at the .05 level, that… b. At the 5% level of significance is the mean … c. At the .10 level of significance, has the selling… .05/2= .025 95% Z-Table Used for finding Confidence Interval: 𝑥 ± Zα/2 X 𝜎 𝓃
- 6. Calculate Null & Alternate Hypothesis Always begin by solving the Alternate Hypothesis first simply by asking “What is the Alternate Hypothesis asking?” In our example case, “Is the mean. (𝝁) 𝐰𝐞𝐢𝐠𝐡𝐭 𝐥𝐞𝐬𝐬 𝐭𝐡𝐚𝐧 𝟏𝟎𝐥𝐛𝐬. “ So, Alternate Hypothesis: The true or actual mean of the population under analysis. H1: 𝜇 < 10 Null Hypothesis: the hypothesized mean of the population under analysis. Ho: 𝜇 ≥ 10
- 7. Decision Rule & Calculate Sample Z Score Reject Ho if Z < -1 .645 Calculate Z: Yes, -2.53 is less than -1.65 T-Score Example
- 8. Write Report Conclusion: We reject the Null Hypothesis (Ho) and conclude the mean weight loss is less than 10 lbs.
- 9. Questions
- 10. References Statistics for Psychology, Fifth Edition, by Arthur Aron, Elaine N. Aron, and Elliot J. Coups. Published by Prentice Hall. Copyright © 2009 by Pearson Education, Inc.
- 12. Z-Table for Problem Back to Slide 4
- 13. Confidence Interval .781.9695% 9.788.22 Back to Slide 5
Editor's Notes
- Work the problem by understanding first!
- The Comparison Distribution (Sampling Distribution) is the distribution that represents the population situation if the null hypothesis is true. Remember, the word Null means, Without value, effect, consequence, or significance; nothings happening, nothing is going on. Hence, it’s their to disprove or try a claim or prediction!
- Critical Values are based on the “Confidence Interval. For example, for a 95% confidence interval (symmetrical distribution), we know 5% is left out there in the tails as 2.5%. Using the formula: Zα/2 or .05/2 = .025. Using the negative Z-Table to find .025 (See Z-Table). The z statistic is an inferential statistic used to determine the number of standard deviations in a standard normal distribution that a sample mean deviates from the population mean stated in the null hypothesis (Current Slide). The obtained value is the value of a test statistic. This value is compared to the critical value(s) of a hypothesis test to make a decision (Slide 7). When the obtained value exceeds a critical value, we decide to reject the null hypothesis; otherwise, we retain the null hypothesis. Note: when dividing critical region percentage, divide by number of tails!
- Make a decision. To make a decision, compare the “sample z-score” (above) to the cutoff Z-score from slide 5. We reject the null hypothesis if the obtained (sample score) value exceeds the critical value. The example here in slide 7, shows that the obtained value (Zα/2 = -2.53) is less than the critical value of -1.65; thus falling into the rejection region. The decision therefore, is to reject the null hypothesis. *Note: Whenever you divide by a fraction you have to multiply by the reciprocal.
- I am 95% confident the population mean is between 8.22 & 9.78.