Suppose we are seeing how well a piece of computer software can predict people\'

Question

Suppose we are seeing how well a piece of computer software can predict people's choices for orange Juice. Let Xi-1 if the predictor is wrong and X-0 if the predictor is correct. The sample mean with unknown parameter p. We would like to understand how our sample mean estimates this unknown quantity (note that our goal is different from the goal of descriptive statistics!) l i is the observed error rate. Assume each i as Bernoulli n (a) How many observations n are needed so that the sample mean is 95% likely to be within 0.1 of p? (b) How many observations n are needed so that the sample mean is 95% likely to be within 0.01 of p? (c) How many observations n are needed so that the sample mean is 99% likely to be within 0.1 of p? (d) How many observations n are needed so that the sample mean is 99% likely to be within 0.01 of p? (e) What is the probability that the sample mean is within 0.1 of p given 500 observations? (f) What is the probability that the sample mean is within 0.01 of p given 500 observations? (g) If you have 30 observations and want to make a statement that holds with 95% probability, how close is the sample mean to the unknown true mean? In other words, determine the tolerance . (h) As in question 1g, find , given 300 observations, for a statement that holds with 95% probability

Explanation / Answer

since estimate of p is not known

n = z^2 /(4e^2)

take z = 1.96 for 95 %

2.576 for 99 %

e = 0.1 for a) and c) and e = 0.01 for b) and d) part

for a)

n = 1.96^2 /(4 *0.1^2)

= 96.04

similarly others

Post rest questions again

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