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Confidence Interval Estimation for a Population Mean

Confidence Interval Estimation for a Population Mean. Lecture 38 Section 10.3 Wed, Mar 30, 2005. Confidence Intervals. To estimate , we will use confidence intervals, as we did when estimating p . The basic form (as well as the theory) is the same: (pt. est.)  (approp. no. of st. devs.).

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Confidence Interval Estimation for a Population Mean

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  1. Confidence Interval Estimation for a Population Mean Lecture 38 Section 10.3 Wed, Mar 30, 2005

  2. Confidence Intervals • To estimate , we will use confidence intervals, as we did when estimating p. • The basic form (as well as the theory) is the same: (pt. est.)  (approp. no. of st. devs.)

  3. Confidence Intervals • Ifx has a normal distribution, then the confidence interval is or  • If (x – )/(s/n) has a t distribution, then the confidence interval is

  4. When to Use Z • If • The population is normal (or nearly normal) and  is known (for any sample size), or • The population is not normal, but the sample size is at least 30, • Then use Z.

  5. When to Use t • If • The population is normal (or nearly normal), and •  is not known, and • The sample size is less than 30, • Then use t.

  6. Table IV • Consider again the t table (Table IV). • The degrees of freedom include every value up to 30, then jump to 40, 60, 120. • If the actual degrees of freedom are • Between 30 and 40, use 30. • Between 40 and 60, use 40. • Between 60 and 120, use 60. • If they are beyond 120, use z.

  7. Example • See Example 10.5, p. 591 – Cereal Boxes. • Use Z. Why? • n = 25. • x = 9.82. • Assume that  = 0.29. • Level of confidence = 95%, so z = 1.96.

  8. Example • The confidence interval is 9.82  (1.96)(0.29/25) = 9.82  0.114 = (9.706, 9.934).

  9. TI-83 – Confidence Intervals • When the standard normal distribution applies, do the following. • Press STAT. • Select TESTS. • Select ZInterval. • A window appears requesting information.

  10. TI-83 – Confidence Intervals • Select Data or Stats. • Assume we selected Stats. • Enter . • Enterx. • Enter n. • Enter the level of confidence. • Select Calculate and press ENTER.

  11. TI-83 – Confidence Intervals • A window appears containing • The title “ZInterval”. • The confidence interval in interval notation. • The sample mean. • The sample size.

  12. Let’s Do It! • Let’s do it! 10.6, p. 593 – How Much Beverage?

  13. Example • See Example 10.6, p. 594 – Empty Seats Imply Dollars Lost. • Should we use Z or t?

  14. TI-83 – Confidence Intervals • To use t, do the following. • Press STAT. • Select TESTS. • Select TInterval. • A window appears requesting information.

  15. TI-83 – Confidence Intervals • Select Data or Stats. • Assume we selected Stats. • Enterx. • Enter s. • Enter n. • Enter the level of confidence. • Select Calculate and press ENTER.

  16. TI-83 – Confidence Intervals • A window appears containing • The title “TInterval”. • The confidence interval in interval notation. • The sample mean. • The sample standard deviation. • The sample size.

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