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Inference Test of Difference of Means

Find the mean number of points for the basketball team and the standard deviation. http://goo.gl/forms/OxRG34i85U. Inference Test of Difference of Means. Section 11.1. Experiment. Separate – boys & girls. Take Pulse rates. Remember…. Independent

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Inference Test of Difference of Means

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  1. Find the mean number of points for the basketball team and the standard deviation. http://goo.gl/forms/OxRG34i85U

  2. Inference Test of Difference of Means Section 11.1

  3. Experiment • Separate – boys & girls. • Take Pulse rates

  4. Remember…. • Independent • Selection of one sample does not influence the selection of the other sample

  5. So if we want to estimate the difference in means between two populations….. • The point estimate is: • So

  6. For the difference of means what is the standard deviation?

  7. The properties of the sampling distribution of • If n1 and n2 are sufficiently large or the populations normal, then the distribution will be approximately normal.

  8. So what is the z-score for the difference in boys and girls pulse rates?

  9. Remember: Use t test if σ is unknown • T-Test statistic Use boxplot to check for normal if samples are small & data given.

  10. So is there a difference between boys and girls?

  11. Assumptions:

  12. D.F. is a little more complicated! A conservative estimate of the P-value can be found by using a df = smaller of either n1-1 or n2-1.

  13. Let’s try one! College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this by asking a random sample of 1296 students who had summer jobs how much they earned. They were then separated into two groups based on gender. Is there a difference in the amount males and females earn?

  14. Amounts different for males & females? Parameter: = true mean amount males earned = true mean amount females earned

  15. Hypothesis or Name Assumptions Use a 2 sample T test of means since σ is unknown • Random: samples chosen randomly • Approximately normal: n1>30 and n2>30. • Independent: more than 6750 males and 6210 females

  16. Test Statistic Obtain a P-value P-value = tcdf (7.81, ∞., 620)*2 ≈ 0

  17. Now to finish it up! Make a decision Reject the Ho since p-value(0) < α (0.05) State a conclusion There’s sufficient evidence to support the claim that there is a difference in the amounts earned by males and females.

  18. Pooling the Data • If you prove the standard deviations are equal then you can pool the data together. • You don’t want to do this….it’s another type of hypothesis test to prove standard deviations equal • Never Pool!

  19. The Formula Sheet

  20. If you bought a used camera in good condition from a friend, would you pay the same as you would if you bought the same item from a stranger.

  21. Don’t forget the boxplot to show normal!

  22. Homework • Worksheet #1

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