Confidence Interval Estimation for a Population Mean Lecture

Confidence Intervals To estimate , we will use confidence intervals, as we did when

Confidence Intervals What is the point estimate for ? n What is the standard

Confidence Intervals n The confidence interval will be or or

When to Use Z n If ¨ The population is normal (or nearly normal)

When to Use t n If ¨ The population is normal (or nearly normal),

Example n n Example 10. 4, p. 641. Construct a 95% confidence interval for

Example Use Z. Why? n n = 25. n x = 9. 82. n

Example n The confidence interval is 9. 82 (1. 96)(0. 29/ 25) = 9.

TI-83 – Confidence Intervals When the standard normal distribution applies, do the following. n

TI-83 – Confidence Intervals Select Data or Stats. n Assume we selected Stats. n

TI-83 – Confidence Intervals A window appears containing n The title “ZInterval”. n The

Example n n Example 10. 5, p. 643. Construct a 99% confidence interval for

Example Should we use Z or t? Why? n n = 61. n x

Example n The confidence interval is 12. 6 (2. 660)(4. 4/ 61) = 12.

TI-83 – Confidence Intervals To use t, do the following. n Press STAT. n

TI-83 – Confidence Intervals A window appears containing n The title “TInterval”. n The

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Confidence Interval Estimation for a Population Mean Lecture 36 Section 10. 4 Wed, Apr 4, 2007

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

Confidence Intervals What is the point estimate for ? n What is the standard deviation for this estimator? n How do we determine the appropriate number of standard deviations? n

Confidence Intervals n The confidence interval will be or or

When to Use Z n If ¨ The population is normal (or nearly normal) and is known, or ¨ The population is not normal, but the sample size is at least 30, n Then use Z.

When to Use t n If ¨ The population is normal (or nearly normal), and ¨ is not known, n Then use t.

Example n n Example 10. 4, p. 641. Construct a 95% confidence interval for the true mean weight of such boxes.

Example Use Z. Why? n n = 25. n x = 9. 82. n Assume that = 0. 29. (Why? ) n Level of confidence = 95%, so z = 1. 96. n

Example n The confidence interval is 9. 82 (1. 96)(0. 29/ 25) = 9. 82 0. 114 = (9. 706, 9. 934).

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

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

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

Example n n Example 10. 5, p. 643. Construct a 99% confidence interval for the mean number of unoccupied seats.

Example Should we use Z or t? Why? n n = 61. n x = 12. 6. n s = 4. 4. n Level of confidence = 99%. Find t. n

Example n The confidence interval is 12. 6 (2. 660)(4. 4/ 61) = 12. 6 1. 499 = (11. 101, 14. 099).

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

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

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