Chapter10_1

Chapter10_1 - .- - - 10 Introduction to Inference ACTIVITY...

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.-- -- --- 10 Introduction to Inference ACTIVITY 10 A Little Tacky! Materials: Small box of thumbtacks When you flip a fair coin, it is equally likely to land "heads" or "tails." Do thumbtacks behave in the same way? In this activity, you will toss a thumb- tack several times and observe whether it comes to rest with the point up (U) or point down (D). The question you are trying to answer is: what pro- portion of the time does a tossed thumbtack settle with its point up (U)? 1. Before you begin the activity, make a guess about what will happen. If you could toss your thumbtack over and over and over, what proportion of all tosses do you think would settle with the point up (U)? 2. Toss your thumbtack 50 times. Record the result of each toss (U or D) in a table like the one shown. In the third column, calculate the proportion of point up (U) tosses you have obtained so far. Toss . Outcome Cumulative proportion of U's 3. Make a scatterplot with the number of tosses on the horizontal axis and the cumulative proportion of U's on the vertical axis. Connect consecutive points with a line segment. Does the overall proportion of U's seem to be approaching a single value? 4. Your set of 50 tosses can be thought of as a simple random sample from the population of all possible tosses of your thumbtack. The parameter p is the (unknown) population proportion of tosses that would land point up (U). What is your best estimate for p? It's 6, the proportion of U's in your 50 thumbtack tosses. Record your value ofb. How does it compare with the conjecture you made in step l? 5. If you tossed your thumbtack 50 more times (don't do it!), would you expect to get the same value of j? In chapter 9, we learned that the val- ues of6 in repeated samples could be described by a sampling distribu- tion. The mean of the sampling distribution 4 is equal to the population proportion p. How far will your sample proportion j be from the true value p? If the sampling distribution is approximately normal, then the 68-95-99.7.rule tells us that about 95% of all j-values will be within two standard deviations of p.
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ACTIVITY 10 A Little Tacky! (continued) 6. The sampling distribution of$ will be approximately normal if n$ 2 and n(l -6) 2 10. Verify that these conditions are satisfied for your sample. 7. Estimate the standard deviation of the sampling distribution by comput- ing /? using your value of$. This is the formula we developed in Chapter 9 with p replaced by$. I. Construct the interval b i 2/9 based on your sample of 50 tosses. This is called a confidence interval for 6. 9. Your teacher will draw a number line with a scale marked off from 0 to 1 that has tick marks every 0.05 units. Draw your confidence interval above the number line. Your classmates will do the same. Do most of the intervals overlap? If so, what values are contained in all of the overlapping intervals?
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This note was uploaded on 12/09/2011 for the course STAT 101 taught by Professor O during the Fall '08 term at Lake Land.

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Chapter10_1 - .- - - 10 Introduction to Inference ACTIVITY...

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