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

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  1. Answers
  2. Give a short summary of the text according to your answers.
  3. Give two examples of events that could shift the demand for labor and the supply of labor. Use two graphs to demonstrate your answers in detail, please.
  4. Match the answers and the questions.
  5. Read the text and find answers to the following questions.
  6. V. Write 12 questions suggesting answers with these patterns. (The questions in Ex. IV may serve as a model.)

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 Unlike the large sample situations, here we do not have an unqualified answer, and central limit theorem is no longer applicable.

 


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Читайте в этой же книге: Sampling distribution of . Its mean and standard deviation | Summary | Exercises | Sampling distribution of a sample variance | Exercises | Introduction | Confidence interval and confidence level | Normally distributed: population variance known | Exercises | Normally distributed: large sample size |
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Exercises| Student’s t distribution

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