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. When using the t distribution, we will assume that the x distribution is normal.

Confidence Interval for the Mean of Small Samples (n  30)

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

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

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

c   ’   ’’ d.f Find the critical value t c for a 95% confidence interval if n = 7.

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

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.

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 =

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

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

THE END OF SECTION 2