Warm up: 11-29-06

1
Warm up 11-29-06
In trying to attract new business, San Diego
County claims that the mean annual income for the
area is greater than 50,000
1. claim__________ Ho____________ H1
___________
2. what kind of tail test? ____________
3. label critical region critical value
4. When do you reject Ho? ______________
5. Write a conclusion when Ho is rejected. 6.
Write a conclusion when Ho is not rejected.
2
Testing a Claim about a Mean for Large Samples
3
Procedure for doing a research study
Do Not Write This

• You have an idea of interest you want to see if
  
• its true

2. You form a claim your hypotheses
3. You set your sample size your a value
4. You determine the critical value(s) critical
region(s) for rejecting Ho
5. You go collect data analyze the sample data
6. You compare the test statistics (obtained from
the sample data) to the critical value(s)
critical region(s)
7. Make a conclusion based on whether Ho is
rejected
4
When were interested in the mean or average,
and were going to use a large sample to collect
our data, the test statistic we use is the
Z-score.
We compare this test statistic to the critical
value(s) critical regions, so that we can
decide whether or not to reject Ho.
5
critical value Z-score
invNorm(area to the left of CV)
too ugly too long
test statistic Z-score
Z (sample mean) (pop. mean)
sample stand. dev.
test statistic using calculator
STAT ?TESTS 1Z-Test Stats m s
x n tails calculate (read z
.)
test statistic Z-score
6
Practice Justine wants to know if the true body
temperature for humans is 98.6 F. Shes going
to do a study using a sample size of 106 people
and a significance level (a) of .05. After
measuring these peoples temperatures, Justine
found a mean of 98.2 F and a standard deviation
of .62.
m 98.6
m 98.6
claim Ho
H1
m 98.6
a
.05
invNorm(.025) - 1.96
.025
.025
- 6.64
TS Z
CVL
CVR
Does TS fall in critical region?
yes
Z -1.96
Z 1.96
Reject Ho?
yes
7
(continued)
m 98.6
m 98.6
claim Ho
H1
m 98.6
a
.05
invNorm(.025) - 1.96
.025
.025
- 6.64
TS Z
CVL
CVR
Does TS fall in critical region?
yes
Z -1.96
Z 1.96
Reject Ho?
yes
conclusion
The claim of the mean body temperature
being 98.6F is rejected.
In other words, Justines study disputes the
common belief that the average body temperature
is 98.6 F.
8
Practice with your group Jenny Craig claims that
you will lose weight in 2 days if you join her
weight loss program. Nathan knows that normal
body weight fluctuates on a daily basis. So,
Nathan is going to test Jenny Craigs claim. He
hypothesizes that if the mean weight loss is
significantly greater than zero, then her program
works. By significant, hes choosing an a .05.
Hes going to sample 33 people. Nathan found a
mean weight loss of .37 lb. with a standard
deviation of .98 lb. for his sample.
claim Ho
H1
a n x
s
tails? CV z
TS z
reject Ho? conclusion
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(ANSWERS)
m gt 0
m 0
claim Ho
H1
m gt 0
a n x
s
.05
33
.37
.98
tails? CV z
TS z
right
1.64
2.17
reject Ho? conclusion
yes
The claim that the mean weight loss is
greater than 0 is supported. In other words,
Jenny Craigs program does seem to work, based on
Nathans study.
10
Classwork p. 372-5 4-6, 9, 16, 19 (dont
follow books instructions for each problem,
test the hypothesis and form a conclusion)