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Chapter 7 Estimation

Chapter 7 Estimation. Chapter 7 ESTIMATION. What if it is impossible or impractical to use a large sample?. Apply the Student ’ s t distribution. The shape of the t distribution depends only the sample size, n, if the basic variable x has a normal distribution.

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Chapter 7 Estimation

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  1. Chapter 7Estimation

  2. Chapter 7ESTIMATION

  3. What if it is impossible or impractical to use a large sample? Apply the Student’s t distribution.

  4. The shape of the t distribution depends only the sample size, n, if the basic variable x has a normal distribution. When using the t distribution,we will assume that the x distribution is normal.

  5. Confidence Intervalfor the Mean of Small Samples (n < 30)

  6. Table 6 in Appendix II gives values of the variable t corresponding to the number of degrees of freedom (d.f.)

  7. Degrees of Freedom d.f. = n – 1 where n = sample size

  8. The t Distribution has a Shape Similar to that of the the Normal Distribution A “t” distribution A Normal distribution

  9. Find the critical value tc for a 95% confidence interval if n = 7.

  10. Confidence Interval for the Mean of Small Samples (n < 30) from Normal Populations c = confidence level (0 < c < 1) tc = critical value for confidence level c, and degrees of freedom = n - 1

  11. The mean weight of eight fish caught in a local lake is 15.7 ounces with a standard deviation of 2.3 ounces. Construct a 90% confidence interval for the mean weight of the population of fishin the lake.

  12. Key Information • Mean = 15.7 ounces • Standard deviation = 2.3 ounces • n = 8, so d.f. = n – 1 = 7 • For c = 0.90, Table t chart • gives t0.90 = 1.8946

  13. The 90% confidence interval is: We can say with 90% confidence that the population mean weight of the fish in the lake is between 14.1594 and 17.2406 ounces.

  14. The 90% confidence interval is: Calculator Computation VARS Statistics TEST H: lower 14.1594 I: upper 17.2406 We can say with 90% confidence that the population mean weight of the fish in the lake is between 14.1594 and 17.2406 ounces.

  15. THE END OF SECTION 2

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