8A

1. A random sample of n = 81 observations has a mean x = 26.2 and a standard deviation s = 3.4. (a) Give the point estimate of the population mean . Find the 95% margin of error for your estimate. (Round your answer to four decimal places.) (b) Find a 90% confidence interval for . (Round your answers to three decimal places.) (c) Find a 90% lower confidence bound for the population mean . (Round your answer to two decimal places.) Why is this bound different from the lower confidence limit in part (b)? (d) How many observations do you need to estimate to within 0.5, with probability equal to 0.95? (Round your answer up to the nearest whole number.)
2. A random sample of n = 500 observations from a binomial population produced x = 290 successes. (a) Find a point estimate for p. Find the 95% margin of error for your estimator. (Round your answer to three decimal places.) (b) Find a 90% confidence interval for p. (Round your answers to three decimal places.) (c) How large a sample is required if you wish to estimate p correct to within 0.05, with probability equal to 0.90? (Compute your sample size calculations to allow for maximum variation. Round your answer up to the nearest whole number.)
3. To study the effect of smoking on blood pressure, the blood pressure of a group of 31 cigarette smokers was measured at the beginning of an experiment and again 5 years later. The sample mean increase, measured in millimeters of mercury, was x = 9.9, and the sample standard deviation was s = 5.1. (a) Estimate the mean increase in blood pressure (in mm of mercury) for cigarette smokers over the time span indicated by the experiment. Find the 95% margin of error (in mm of mercury). (Round your answer to two decimal places.) (b) Describe the population associated with the mean that you have estimated.
4. Based on repeated measurements of the iodine concentration in a solution, a chemist reports the concentration as 4.614, with an "error margin of 0.005." (a) How would you interpret the chemist's "error margin"?(b) If the reported concentration is based on a random sample of n = 42 measurements, with a sample standard deviation s = 0.016, would you agree that the chemist's "error margin" is 0.005?
5. If it is assumed that the heights of men are normally distributed with a standard deviation of 3.0 inches, how large a sample should be taken to be fairly sure (probability 0.95) that the sample mean does not differ from the true mean (population mean) by more than 0.10 in absolute value? (Round your answer up to the nearest whole number.)