Suppose you have been hired by the Better Business Bureau (BBB) to investigate the settlement ratio of the complaints they have received. You plan to select a sample of n complaints to estimate the proportion of complaints the BBB is able to settle. We use p to denote the percentage or proportion of complaints settled among all the complaints that the BBB has received. Q1) Let Y be the random variable, which indicates whether a complaint is settled. Without loss of generality, let Y be 1 if a complaint is settle, the probability of which is p; 0 if not settled. What probability distribution does Y follow? Compute its mean and standard deviation. Q2) Now suppose you select a random sample of n complaints and find that p ̅ of them have been settled (not surprisingly, p ̅ is called the sample proportion). Assume the sample size n is sufficiently large. What do we know about the probability distribution of p ̅ (sampling distribution of the sample proportion)?
Suppose you have been hired by the Better Business Bureau (BBB) to investigate the settlement ratio of the complaints they have received. You plan to select a sample of n complaints to estimate the proportion of complaints the BBB is able to settle. We use p to denote the percentage or proportion of complaints settled among all the complaints that the BBB has received.
Q1)
Let Y be the random variable, which indicates whether a complaint is settled. Without loss of generality, let Y be 1 if a complaint is settle, the
Q2)
Now suppose you select a random sample of n complaints and find that p ̅ of them have been settled (not surprisingly, p ̅ is called the sample proportion). Assume the
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