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1. What role does the central limit theorem play in the construction of a confidence interval for the population mean?

2. In using the standard normal distribution to construct a confidence interval for the population mean, what two assumptions are necessary if the sample size is less than 30?

3. The following data values are a simple random sample from a population that is normally distributed, with C2 5 25.0: 47, 43, 33, 42, 34, and 41. Construct and interpret the 95% and 99% confidence intervals for the population mean.

4. A simple random sample of 30 has been collected from a population for which it is known that C 5 10.0. The sample mean has been calculated as 240.0. Construct and interpret the 90% and 95% confidence intervals for the population mean.

5. A simple random sample of 25 has been collected from a normally distributed population for which it is known that C 5 17.0. The sample mean has been calculated as 342.0, and the sample standard deviation is s 5 14.9. Construct and interpret the 95% and 99% confidence intervals for the population mean.

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