1. Chapter 7 Estimation

2. Chapter 7 ESTIMATION

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 Interval for 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. c   ’   ’’ d.f. 0.900 0.050 0.100 0.950 0.025 0.050 0.980 0.010 0.020 0.990 0.005 0.010... 6...1.94322.44693.14273.7074 7...1.89462.36462.99803.4995 8...1.85952.30602.89653.3554 Find the critical value t c 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) t c = 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 fish in 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 t 0.90 = 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: 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. Calculator Computation VARS Statistics TEST H: lower 14.1594 I: upper 17.2406

15. THE END OF SECTION 2