1. Chapter 5
Hypothesis Tests With
Means of Samples
Part 2: Sept. 9, 2014

2. Estimating μ In estimating a population mean we have 2 options:
1) Point estimates give specific #
Example:
Accuracy of such a point estimate of the pop mean – ok, but not great
Our sample may be unrepresentative, etc.

3. Estimating μ (cont.)
2) Interval estimates – provide range where you think pop mean may fall
Ex) Given M=5.9 (which = μM), and std dev = .2 (which is σM), and assuming a normal curve…
We’d expect 34% of pop means to fall b/w 5.9 & 6.1 (+1 SD) and another 34% b/w 5.9 & 5.7 (-1 SD)
68% between 5.7 and 6.1  consider this a 68% confidence interval
What does that mean?

4. 95% Confidence Intervals (analogous to alpha = .05)
But 68% confident not that great…more interest in 95% or 99% confidence.
Standard to use 95% or 99%
Use normal curve table & find z score cutoffs for .05 significance level, 2-tailed test:
Change these to raw scores for our example
Using x = z(σM) + M , what scores do you get?
What is the final 95% confidence interval for this example and what does it mean?

5. 99% Confidence Intervals (analogous to alpha = .01)
For 99% interval (2-tailed), find z score cutoffs in normal curve table:
Change these to raw scores for our example
x = z(σM) + M, what do you get?
What is the 99% confidence interval here? What does it mean?

6. Confidence Intervals (CI)
Notice the wider interval for 99% compared to narrower interval for 95%
Wider more likely you’re right and you include the actual mean in that interval

7. 1 vs. 2 tailed estimates
Also note that we can calculate CIs for 1-tailed tests:
You will still calculate 2 scores to give a range of confidence.
What changes is the relevant z score…
95% CI for ‘crashed’ example:
Z score cutoff will be 1.64, so use conversion formula:
X = Z(σM) + M and then x = -Z(σM) + M , so…
Resulting 1-tailed 95% CI is…
Narrower or wider interval than 2-tailed 95% CI?

8. Cutoff Scores for CI’s
As a shortcut, you may memorize or refer to these cutoff scores when computing CI’s – these will never change!
Cutoff scores most often used:
For a 95% CI, 1-tailed = 1.64 and –1.64
95% CI, 2-tailed = 1.96 and –1.96
99% CI, 1-tailed = 2.33 and –2.33
99% CI, 2-tailed = 2.57 and –2.57