In Example 1.4 we looked to see whether the competent- face method could be used to predict the results of Senate races. We found this method worked in 23 out of 32 races. When testing to see if the probability of this method working is more than 0.50, we obtained a null distribution similar to that shown.

a. Using the information provided above, determine a 2SD 95% confidence interval for the probability the competentface method will work.
b. Based on your confi dence interval, can you conclude the probability the competent-face method will work is greater than 50%? Explain.
c. Why shouldn€™t a theory-based approach be used to compute the confidence interval for these data?

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Probability of heads: 0.5 32 Number of tosses: Number of repetitions: 1000 M Animate Toss Coins Total = 1000 180 Mean = 0.501 SD = 0.090 120 8.19 0.28 0.38 0.47 0.56 0.66 0.75