Chapter 7
Hypothesis Tests With
Means of Samples – Part 2
Oct. 6
Estimating μ
 In estimating a population mean we have 2 options:
– 1) Point estimates give specific #
– In the example from Tues (problem #9), we found a
sample M=5.9 for the group of students who read about
the accident w/ the word “crashed”.
– Our estimate for μ (pop mean for students who get ‘crash’
wording) should = 5.9. It’s based on our previous sample,
which is the best guess
 Accuracy of such a point estimate of the pop mean –
ok, but not great
– Our sample may be unrepresentative, etc.
Estimating μ (cont.)
 2) Interval estimates – provide range where
you think pop mean may fall
– Ex) Given M=5.9 (which = μM), and std error = .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/Std error) and another 34% b/w 5.9 &
5.7 (-1 SD/Std error)
– 68% between 5.7 and 6.1  consider this a 68%
confidence interval
• You can be 68% confident that a new population of
students who get “crashed” manipulation would have
a mean between 5.7 & 6.1
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%
– For 95% interval, we’re left with 47.5% of scores
(95/2) on each side of the mean up to our cutoff
– Use normal curve table, find z=1.96 and –1.96 for
those %s (note – this is 2-tailed!)
– Change these to raw scores for our example (x =
z(σM) + M) , get:
• x = 1.96(.2) + 5.9 = 6.29… and
• x = -1.96(.2) + 5.9 = 5.51
– 95% confident true pop mean for ‘crash’ pop lies
b/w 5.51 and 6.29
99% Confidence Intervals
(analogous to alpha = .01)
 For 99% interval, area of curve on each
side of mean up to cutoff points = 49.5%
(99/2), use normal table, find z=2.57 and
–2.57 for those %. (note – this is 2-tailed!)
 Change these to raw scores for our
example (x = z(σM) + M) , get:
– x = 2.57(.2) + 5.9 = 6.41… and
– x = -2.57(.2) + 5.9 = 5.39
 99% confident true pop mean for ‘crash’
pop lies b/w 5.39 and 6.41
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
 Can be used for hyp testing:
– Here’s the Rule: if the CI does not contain
mean from null hyp (which is μ), 
Reject Null.
CI and Hypothesis Testing (cont.)
 Our ex) – 95% conf int (5.51, 6.29) does
not include 5.50 (see Tues example) ,
so reject Null & conclude our 5.9
sample mean is unlikely to come from
that population (it differs from the pop)
 But 99% conf int does include 5.50, so
sample group would not differ if we use
.01 signif level
1 vs. 2 tailed estimates
 Also note that we can calculate CIs for 1-tailed
tests:
– 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…
– X = 1.64 (.2) + M = 6.23 and
– X = -1.64 (.2) + M = 5.57
• We are 95% confident for this 1 tailed test that the true
pop mean is betw 5.57 and 6.23
• Notice that a 95% 1-tailed test gives a narrower CI than
the 95% 2-tailed test
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 or –1.64
– 95% CI, 2-tailed = 1.96 and –1.96
– 99% CI, 1-tailed = 2.33 or –2.33
– 99% CI, 2-tailed = 2.57 and –2.57
Activity 4 (cont.)

Finish #8 at end of Ch 7 from Tues.

In attempt to decrease reaction time, 25 women
participate in training. After training, women have
M=1.5 sec; gen population μ = 1.8 with σ = .5
1. (If you completed Tues. activity, you’ve already done
this) Carry out 5 hyp testing steps (use alpha=.05) (and
be sure to draw the comparison distribution to help
you!)
2. (New!) Figure the 95% CI and interpret its meaning.
Does it lead to same conclusion about rejecting/failing
to reject the null as Part 1?
Turn in this along with part 1 from Tues.