A random sample of 90 observations produced a mean 25.9 and a standard deviation 2.7
1. A random sample of 90 observations produced a mean 25.9 and a standard deviation 2.7. Find an approximate 95% confidence interval for the population mean.
2. A study conducted showed that a random sample of 15 of newborns on the average weighed 6.7 pounds with a standard deviation of 1.2 pounds. Assume the distribution of these weights is approximately normal. Find a 95% confidence interval for the population mean.
3. A city wants to estimate the mean number of gallons of water use per household per day. From experience, it is known that the standard deviation of such usage is 40 gallons. The city intends to collect a random sample and monitor the water usage.
(a) Suppose that they take a sample of size 196 with mean 300 gallons, find a 90% confidence interval for the population mean.
(b) Suppose the city needs to be within 5 gallons of the true value with a 95% confidence. How large a sample will be needed?
(c) Suppose they take a sample of size 150. With what level of certainty can they ensure that the error in their estimate of the mean usage is no more than 4.5?
4. A random sample of eight tax filers who completed the forms themselves found that they had 1, 3, 0, 4, 2, 3, 1, and 2 mistakes on their forms. Find a 90% confidence interval for the mean number of mistakes for tax filers that completed the forms themselves.
5. A random sample of size 225 yielded a sample proportion .46.
(a) Is the sample size large enough to construct a Large-Sample confidence interval for p? (b) Construct a 95% confidence interval for p.
6. Suppose you are trying to estimate the proportion of college students that live off campus their sophomore year. How large a sample will be needed to be 99% confident that our estimate will be off by no more than .05 if
(a) A similar study was done 5 years ago that indicated that 60% of sophomores live off campus? (b) No prior knowledge is known?
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