sampling sizes. an important, but offen underused, part of statistics uses our knowledge about how confidence intervals are created to estimate teh sample size needed to achieve a certain level of accuracy in our results. by making sure that a large enough sample will be collected before going through the process we can save time and money, with the added benefit of making you look smart in front of your boss! consider a population having standard deviation equal to 10. we wish to estimate the mean of this population.
a.) how large a random sample is needed to construct a 95% confidence interval for themean of this population with a margin of error equal to 1
b.) suppose that we now take a random sample of the size we have determined in part (a). if we obtain a sample mean x equal to 295, calculate the 95% confidence interval for the population mean.
c.) if i only required the interval in (a) to have a margin of error equal to 2, how large a random sample is needed (use the same confidence level)?
d.) suppose that we now take a random sample of the size we have determined in part c) if we obtain a sample mean x equal to 295, calculate the 95% confidence interval for the population mean. what is the interval's margin of error?
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