HOW MUCH SLEEP DID YOU GET LAST
NIGHT?
1.
2.
3.
4.
5.
6.
<6
6
7
8
9
>9
29%
29%
14%
14%
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1- 1
0%
1
14%
2
3
4
5
6
SLEEP AND TECHNOLOGY
“43 percent of Americans say they rarely or never get a
good night’s sleep during the week”
 “Nearly everyone, 95 percent, use electronics (like TV,
computer, or cell phone) within the hour just before
bed”
 “Researchers caution that the use of such devices are
particularly harmful to the sleep-onset process, since
the artificial light can suppress the release of
melatonin which is our sleep hormone.”
 http://www.scientificamerican.com/podcast/episode.cfm
?id=electornic-gadgets-before-bed-can-h-11-03-07

CHAPTER 23
Inference About Means
A CONFIDENCE INTERVAL FOR MEANS? (CONT.)
One-sample t-interval for the mean

When the conditions are met, we are ready to find the
confidence interval for the population mean, μ.

The confidence interval is
 SE  y 

n1
where the standard error of the mean is
y t

s
SE  y  
n
t*
The critical value n1 depends on the particular
confidence level, C, that you specify and on the number
of degrees of freedom, n – 1, which we get from the
sample size.
2. MODEL



All models require assumptions, so state the
assumptions and check any corresponding
conditions.
Assumptions you will test

Independence

Randomization

10% condition

Normality
Determine Alpha Level
Slide 1- 5
HW-11 PROBLEM 5



A nutrition lab test 50 ‘reduced sodium’ hot dogs,
finding that the mean sodium content is 318mg
with a standard deviation of 36mg.
You want to create a 95% confidence interval to
test your hypothesis.
What assumptions have you made? Are these
assumptions correct?
Slide
1- 6
WHAT ASSUMPTION HAVE WE MADE IN
THIS INFERENCE?
1.
2.
3.
We have assumed that the hot dogs weights are
NOT multimodal and that the distribution of
the population of hot dog weights does not
contain any outliers.
We have assumed that the hot dog weights are
random and that the distribution of the
population of hot dog weights is not biased.
We have assumed that the hot dog weights are
independent and that the distribution of the
population of hot dogs is normal
Slide
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%
“A LAB TESTS 50 HOT DOGS”. IS THE
RANDOMIZATION CONDITION SATISFIED?
1.
2.
7%
3.
%
3%
4.
No, because the hot dogs came from the same
package
No, there is evidence to believe that the hot
dogs were not sampled at random
Yes, there is definitely evidence to believe that
the hot dogs were sampled at random
We don’t know that the hot dogs were sampled
at random, but it is reasonable to think that
they were
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1- 8
IS THE 10% CONDITION SATISFIED?
No, 50 hot dogs are more than 10% of all hot
dogs.
2.
Yes, 50 hot dogs are more than 10% of all hot
7% dogs.
3.
No, 50 hot dogs are less than 10% of all hot
14% dogs.
4.
Yes, 50 hot dogs are less than 10% of all hot
79% dogs.
1.
0%
Slide
1- 9
EXPLAIN CLEARLY WHAT YOUR INTERVAL
MEANS
7% 1. 95% of the sodium content in this type of ‘reduced
sodium’ hot dog will be contained in the interval
2.
We are 95% confident that the interval contains the
true mean sodium content for this type of hot dog.
79%
3.
The interval contains the true mean sodium content
in this type of ‘reduce sodium’ hot dogs 95% of the
time.
7%
4.
95% of all ‘reduced sodium’ hot dogs will have a mean
sodium content that falls within the interval
7%
Slide
1- 10
HW 11 - PROBLEM 7



Students investigating the packaging potato
chips purchased 6 bags of chips from Kroger
marked with a net weight of 28.1 grams.
They weighed the contents of each bag, recording
the weight as follows:
29.2, 28.2, 29.1, 28.5, 28.8, 28.6
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IS THE RANDOMIZATION CONDITION
SATISFIED?
We don’t know that the bag of chips were
0% sampled at random, but it is reasonable to
think that they were
2.
No, the 6 bags were not selected at random, but
100%it is reasonable to think that these bags are
representative of the population
3.
Yes, there is definitely evidence to believe that
0% the bags of chips were sampled at random.
1.
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1- 12
IS THE 10% CONDITION SATISFIED?
Yes, 6 bags of chips are more than 10% of the
populations of all bags of chips
2.
Yes, 6 bags of chips are less than 10% of the
100%populations of all bags of chips
3.
No, 6 bags of chips are more than 10% of the
0% populations of all bags of chips
4.
No, 6 bags of chips are less than 10% of the
populations of all bags of chips
0%
1.
0%
Slide
1- 13
DATA: 29.2, 28.2, 29.1, 28.5, 28.8, 28.6

Find the
Sample mean
 Sample standard deviation


Create

95% confidence interval for the mean weight
Slide
1- 14
THIS DATA IS ON THE WEIGHT OF A BAG OF
POTATO CHIPS. INTERPRET THE 95% CI
95% of all bags of chips will have a mean
weight that falls within the interval
2.
95% of the chips will be contained in the
0%
interval
3.
The interval contains the true mean weight of
0%
the contents of a bag of chips 95% of the time
4.
We are 95% confident that the interval contains
100% the true mean weight of the contents of a bag of
chips.
0%1.
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1- 15
COMMENT ON THE COMPANY’S STATE NET
WEIGHT OF 28.1G
Since the interval is ABOVE the stated weight of 28.1
grams, there is evidence that the company is filling
92% the bags to MORE than the stated weight, ON
AVERGAGE.
2.
Since the interval is BELOW the stated weight of
28.1 grams, there is evidence that the company is
8% filling the bags to LESS than the stated weight, ON
AVERGAGE.
3.
Since the interval CONTAINS the stated weight of
28.1 grams, there is evidence that the company is
0% filling the bags to the stated weight, ON
AVERGAGE.
1.
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1- 16
HW11- PROBLEM 10


A company announced a ‘1000 Chips Trial’
claiming that every 18-ounce bag of its cookies
contained at least 1,000 chocolate chips.
Students purchased random bags of cookies from
different stores and counted the number of chips
in each bag. Data were recorded to test the
claim.
STUDENTS PURCHASED RANDOM BAGS OF
COOKIES FROM DIFFERENT STORES. IS THE
RANDOMIZATION CONDITION MET?
100%
1.
2.
Yes
No
0%
1
2
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STUDENTS PURCHASED COOKIES FROM
DIFFERENT STORES. IS THE INDEPENDENCE
ASSUMPTION MET?
1.
2.
Yes
No
91%
9%
Slide
1- 19
1
2
IS THE 10% CONDITION MET?
1.
2.
Yes
No
100%
0%
1
2
Slide
1- 20
IS THE DATA NEARLY NORMAL?
1.
2.
Yes
No
100%
0%
1
2
Slide
1- 21
DATA – CREATE A 95% CI
1022
1142
1120
1269
1276
1228
1202
1317
1325
1491
Slide
1- 22
THE COMPANY CLAIMS AT LEAST 1000 CHIPS IN
EVERY BAG. WHAT WOULD YOU CONCLUDE?
69%
1.
2.
3.
The company’s claim is
true
The company’s claim is
false
We cannot test this
claim
31%
0% Slide
1- 23
1
2
3
HW 11 - PROBLEM 9
One of the important factors in auto safety is the
weight of the vehicle.
 Insurance companies are interested in knowing the
average weight of cars currently licensed. They believe
it is 3,000 lbs. (i.e. hypothesize).
 To test this belief, they checked a random sample of 91
cars and found:
 Mean weight 2,855lbs.
 SD 531.5lbs
 Is this strong evidence that the mean weight of all cars
is NOT 3,000lbs.?

Slide
1- 24
IS THIS STRONG EVIDENCE THAT THE MEAN
WEIGHT OF ALL CARS IS NOT 3000LBS?
Yes, there is sufficient evidence the mean is
different from 3000
0%2. No, there is sufficient evidence the mean is
different from 3000
3.
Yes, there is NOT sufficient evidence the mean
0%
is different from 3000
4.
No, there is NOT sufficient evidence the mean
100% is different from 3000
0%1.
Slide
1- 25
HW 11 -PROBLEM 11
Slide
1- 26
TEST THE HYPOTHESIS THAT THE MEAN
COMPLETION TIME FOR THIS MAZE IS 60 SEC
1.
2.
3.
4.
Reject null, there is sufficient evidence to
suggest the mean time is NOT 60 sec.
Reject null, there is NOT sufficient evidence to
suggest the mean time is NOT 60 sec.
Fail to reject null, there is sufficient evidence to
suggest the mean time is NOT 60 sec.
Fail to reject null, there is NOT sufficient
evidence to suggest the mean time is NOT 60
sec.
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1- 27
ELIMINATE THE OUTLIER THEN, TEST THE
HYPOTHESIS THAT THE MEAN COMPLETION
TIME FOR THIS MAZE IS 60 SEC
1.
2.
3.
4.
Reject null, there is sufficient evidence to suggest the
mean time is NOT 60 sec.
Reject null, there is NOT sufficient evidence to
suggest the mean time is NOT 60 sec.
Fail to reject null, there is sufficient evidence to
suggest the mean time is NOT 60 sec.
Fail to reject null, there is NOT sufficient evidence to
suggest the mean time is NOT 60 sec.
Slide
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DO YOU THINK THIS MAZE MEETS THE
“ONE-MINUTE AVERAGE” REQUIREMENT?
There is NOT evidence that the mean time required for
rats to complete the maze is different from 60s. The maze
0%
meets the requirements.
2.
There is evidence that the mean time required for rats to
complete the maze is different from 60s. The maze meets
10%the requirements.
3.
There is evidence that the mean time required for rats to
complete the maze is different from 60s. The maze DOES
90%NOT meet the requirements.
4.
There is NOT evidence that the mean time required for
rats to complete the maze is different from 60s. The maze
0% DOES NOT meet the requirements.
Slide
1.
1- 29
UPCOMING IN CLASS


Homework #11 due Monday
Start working on the final step of your data
project

Quiz #6 next Thursday

Exam #2 is Thursday April 26th.
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