Confidence Intervals…continued

How confidence intervals behave What we would like:

High confidence Small margin of error

Remember: For confidence intervals for population mean

margin of error =

Margin of error = How can we make it smaller?

1. Make z* smaller.

2. gets smaller.

3. n gets larger.

Example 10.6, p. 550 Suppose that the manufacturer in Example 10.5

(p.546) wants 99% confidence rather than 90%. The critical value for 99% confidence is z* = 2.575. The 99% confidence interval for µ based on an SRS of 20 video monitors with mean mV is

306 . 3 ±(2 .575)43√20

=¿306 . 3 ± 24 .8=¿(281 . 5 , 331. 1)

From Example 10.5, we had a margin of error of 15.8, giving the 90% confidence interval of

Example 10.6, p. 550 Suppose that the manufacturer in Example 10.5 (p.546) wants 99%

confidence rather than 90%. The critical value for 99% confidence is z* = 2.575. The 99% confidence interval for µ based on an SRS of 20 video monitors with mean mV is

99 % confidence interval of 90% confidence interval of

Margin of error So how do we get a high confidence level with a

small margin of error?PLAN AHEAD!!!

We get to choose our sample size!!!!

Determining Sample Size Example 10.7, p. 551Company management wants a report of the mean screen tension for the day’s production accurate to within ±5 mV with 95% confidence. How large a sample of video monitors must be measured to comply with this request?

So we want the margin of error (m) to be less than 5.

Example 10.7, p. 551For the a 95% confidence level, the critical value is .

Example 10.5 told us that .

So take a sample of at 285 video screens.

Sample Size for Desired Margin of Error

To determine the sample size n that will yield a confidence interval for a population mean with a specified margin of error m, set the expression for the margin of error to be less than or equal to m and solve for n:

Some Cautions with Confidence Intervals

Any formula is correct only in specific circumstances: (some are listed on p. 553 in your book)

• Data must be from an SRS from the population.

• Formula not correct for more complex sampling designs

• Fancy formulas can’t rescue badly produced data

• Outliers can have a large effect on the confidence interval

Some Cautions with Confidence Intervals

Most importantly: The margin of error in a confidence interval covers only random sampling errors.

Homework P. 550: 10.8, 10.9 P. 552: 10.12 P. 554: 10.15, 10.17

DUE: Friday