Ch 8 1 Confidence Intervals The Basics confidence

Ch. 8 -1 Confidence Intervals: The Basics

confidence intervals significance tests Introducing confidence intervals visually. I need a volunteer.

current AP Stats students 4 students Based on our sample, we estimate the mean exam score is ___

point estimator parameter point estimate statistic What does this remind you of? Ch. 7 sampling distribution normal because pop. dist. is normal

______ Write this every time!! REMEMBER THE WORDING!! context confident

If we were to repeat the sampling procedure many times, about 95% of the confidence intervals computed would capture the mean final exam score. Use the Java applet to take many samples of size 4 to make many confidence intervals. Draw the picture to the right.

How much does the fat content of Brand X hot dogs vary? To find out, researchers measured the fat content (in grams) of a random sample of 10 Brand X hot dogs. A 95% confidence interval for the population standard deviation σ is 2. 84 to 7. 55. 1. Interpret the confidence interval. We are 95% confident that the interval from 2. 84 to 7. 55 g captures the true standard deviation of the fat content of Brand X hot dogs. 2. Interpret the confidence level. If we were to repeat the sampling procedure many times, about 95% of the confidence intervals computed would capture the population standard deviation. 3. True or false: The interval from 2. 84 to 7. 55 has a 95% chance of containing the actual population standard deviation σ. Justify your answer. False. The probability is either 1 (if the interval does contain the true st dev) or 0 (if it doesn’t).

Shorter interval, lower % hit Bigger interval, highest % hit (that you’ll be dealing with) increasing increases

Margin of Error depends on critical value and std dev. 95% confidence 99. 7% confidence General Formula: The critical value depends on the confidence level. We will be calculating different critical values in Ch. 8 -2 and 8 -3. What kind of critical values would reduce the margin of error? lower values increasing sample size Lower standard deviation by ___________ less variability Larger samples give more precise estimates ________ Why don’t we always get large sample sizes in the real world? Very costly and time-consuming

randomized random normal the population 10% condition

SRS stratified random sampling cluster random assignment