Find the mean number of points for the basketball team and the standard deviation. Player Points St. Dev. John 5 1 Tim 8 2 Ed 12 4 Marcus 10 3 Demetrius 14 4 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 So if we want to estimate the difference in means between two populations….. The point estimate is: So For the difference of means what is the standard deviation? The properties of the sampling distribution of x x 1 x x 1 1 x2 x2 2 1 2 1 2 n1 2 2 n2 If n1 and n2 are sufficiently large or the populations normal, then the distribution will be approximately normal. So what is the z-score for the difference in boys and girls pulse rates? Remember: Use t test if σ is unknown T-Test statistic t x 1 x 2 1 2 2 s1 n1 Use boxplot to check for normal if samples are small & data given. 2 s2 n2 So is there a difference between boys and girls? Assumptions: D.F. is a little more complicated! s s n n 2 1 2 1 df 2 2 2 2 2 s s n n 1 2 n1 1 n2 1 2 1 2 2 A conservative estimate of the P-value can be found by using a df = smaller of either n1-1 or n2-1. 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? Amounts different for males & females? n mean st. dev. Males 675 $1884.52 $1368.37 Females 621 $1360.39 $1037.46 Parameter: 1 = true mean amount males earned 2 = true mean amount females earned Hypothesis or Assumptions 1. Random: samples chosen randomly 2. Approximately normal: n1>30 and n2>30. 3. Independent: more than 6750 males and 6210 females Name Use a 2 sample T test of means since σ is unknown Test Statistic Obtain a P-value P-value = tcdf (7.81, ∞., 620)*2 ≈ 0 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. 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! The Formula Sheet 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. Friend Stranger 275 260 300 250 260 175 300 130 255 200 275 225 290 240 300 Don’t forget the boxplot to show normal! Homework Worksheet #1

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