Answers. 6.5. Confidence intervals for the mean of a normal distribution:

1. (84.63, 88.38); 2. (0.854, 0.876); 3. (182.2, 197.8); 4. a) (14.53, 17.47);

b) (14.76, 17.24); c) (14.96, 17.04); 5. a) 53.94 to 56.70; b) 56.17 to 58.63; c) 54.95 to 57.55; 6. a) ($79 595, $81 849); b) ($64 093, $66 422);

7. 91.83 to 100.17; 8. 0.8502 or about 85 %.

6.5. Confidence intervals for the mean of a normal distribution:

Population variance unknown: small sample size

In previous topics we discussed inferences about a population mean when a large sample is available. Those methods are deeply rooted in the central limit theorem, which guarantees that the distribution of is approximately normal.

Many investigations require statistical inferences to be drawn from small samples (n <30). Since the sample mean will still be used for inferences about , we must address the question, “what is the sampling distribution of when n is not large?”. Unlike the large sample situations, here we do not have an unqualified answer, and central limit theorem is no longer applicable.

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