Confidence Interval Estimation for a Population Mean Lecture 36 Section 10.4 Mon, Nov 5, 2007

(pt. est.)  (appropriate no. of st. devs.) 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 as before: (pt. est.)  (appropriate no. of st. devs.)

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

Confidence Intervals The confidence interval will be or

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

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

Example Example 10.4, p. 641. Construct a 95% confidence interval for the true mean weight of such boxes.

Example Use Z. (Why?) n = 25. x = 9.82. Assume that  = 0.29. (Why?) Level of confidence = 95%, so z = 1.96.

Example The confidence interval is

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

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.

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

Example 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 = 61. x = 12.6. s = 4.4. Level of confidence = 99%. Find t.

Example The confidence interval is

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

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.

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.