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’s apply the results above and derive some confidence intervals. Note that the population proportion p is unknown. In order to compute the standard error , we substitute for p. As long as the sample size n is sufficiently large, a normal distribution would approximate the sample distribution of the sample proportion well enough. Suppose the sample proportion you’ve found is 0.6. Find a 95% confidence interval of the population proportion, if the sample size is 36, 100, and 400, respectively. What effect does the sample size n have on the resulting confidence interval? Q2) It is often the case that we have a target for margin of error in mind and we want to know the sample size needed to guarantee such a margin of error when the confidence level is given. Use the formula to compute the sample sizes needed when the respective value of m is 1%, 3%, and 5% and the respective confidence level is 90%, 95%, and 99%.
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’s apply the results above and derive some confidence intervals. Note that the population proportion p is unknown. In order to compute the standard error , we substitute for p. As long as the
Q2)
It is often the case that we have a target for margin of error in mind and we want to know the sample size needed to guarantee such a margin of error when the confidence level is given. Use the formula to compute the sample sizes needed when the respective value of m is 1%, 3%, and 5% and the respective confidence level is 90%, 95%, and 99%.
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