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Find the mean number of points for the basketball team and the standard deviation.

Find the mean number of points for the basketball team and the standard deviation. Inference Test of Difference of Means. Section 11.1. Experiment. Separate – boys & girls. Take Pulse rates. Remember…. Independent Selection of one sample does not influence the selection of the other sample.

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Find the mean number of points for the basketball team and the standard deviation.

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  1. Find the mean number of points for the basketball team and the standard deviation.

  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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