Transcript No Slide Title
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2.
3.
D
O YOU BELIEVE THE MAYOR OF SMOKED CRACK
?
T
ORONTO Yes No
33% 33%
This is not relevant to how great of a mayor he is.
33% 1 2 3 Slide 1- 1
C
HAPTER
17 &18
Inference About Means
A C ONFIDENCE I NTERVAL FOR M EANS ? ( 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
y
t
n
1 sample size.
SE y t
s n
confidence level, C, that you specify and on the number of degrees of freedom, n – 1, which we get from the
C
HIPS
P
ROBLEM 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
Slide 1- 4
D
ATA
: 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
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0% 0% 0% 0%
T
HIS DATA IS ON THE WEIGHT OF A BAG OF POTATO CHIPS
. I
NTERPRET THE
95% CI
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2.
3.
4.
95% of all bags of chips will have a mean weight that falls within the interval 95% of the chips will be contained in the interval The interval contains the true mean weight of the contents of a bag of chips 95% of the time We are 95% confident that the interval contains the true mean weight of the contents of a bag of chips.
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0% 0% 0%
C
OMMENT ON THE COMPANY
’
S STATE NET
28.1
G 1.
Since the interval is ABOVE the stated weight of 28.1 grams, there is evidence that the company is filling the bags to MORE than the stated weight, ON AVERGAGE.
2.
3.
Since the interval is BELOW the stated weight of 28.1 grams, there is evidence that the company is filling the bags to LESS than the stated weight, ON AVERGAGE.
Since the interval CONTAINS the stated weight of 28.1 grams, there is evidence that the company is filling the bags to the stated weight, ON AVERGAGE.
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T
HE T
-
DISTRIBUTION AND OUR SAMPLE
A practical sampling distribution model for means
When the conditions are met, the standardized sample mean
t
y
follows a Student’s t-model with n – 1 degrees of freedom. We estimate the standard error with
s n
Slide 1- 8
T
EST
R
ULES If |t| > t*, then reject H 0 If |t| < t*,then fail to reject H 0 If α > p-value, then reject H 0 If α < p-value, then fail to reject H 0
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F
IND P
-
VALUES Online Program http://www.tutor homework.com/statistics_tables/statistics_tables.
html TI-83/TI-84/TI-89 http://www.stat.osu.edu/~stated/resources/calc_h ow.php
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U
SING YOUR SOFTWARE
,
FIND THE FOLLOWING P
-
VALUES What is the p-value for t≥2.61 with 4 degrees of freedom?
What is the p-value for |t|>1.81 with 21 degrees of freedom?
What is the p-value for |t|<1.53 with 21 degrees of freedom?
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C
HOCOLATE
C
HIP
P
ROBLEM 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.
D
ATA 1022 1142 1120 1269 1276 1228 1202 1317 1325 1491
– C
REATE A
95% CI
Slide 1- 13
T
EST THE HYPOTHESIS THAT THE AVERAGE NUMBER OF CHIPS IN A BAG IS GREATER THAN
1,000. W
HAT WOULD YOU CONCLUDE
?
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2.
3.
The average number of chips is 1,000.
We have evidence that the average number of chips is greater than 1,000.
We fail to find evidence that the average number of chips is different from 1,000.
1 0% 0% 2 0% Slide 1- 14 3
T
EST THE HYPOTHESIS
AGAIN
USING THE T
-
SCORE METHOD WITH A SIGNIFICANCE LEVEL OF
0.01. W
HAT WOULD YOU CONCLUDE
?
1.
2.
3.
The average number of chips is 1,000.
We have evidence that the average number of chips is greater than 1,000.
We fail to find evidence that the average number of chips is different from 1,000.
1 0% 0% 2 0% Slide 1- 15 3
T
HE COMPANY CLAIMS AT LEAST
1000 C
HIPS IN
EVERY
BAG
. W
HAT WOULD YOU CONCLUDE
?
1.
2.
3.
The company’s claim is true The company’s claim is false We cannot test this claim
1 0% 0% 2 0% Slide 1- 16 3
T
HE T
-
DISTRIBUTION AND OUR SAMPLE
A practical sampling distribution model for means
When the conditions are met, the standardized sample mean
t
y
follows a Student’s t-model with n – 1 degrees of freedom. We estimate the standard error with
s n
Slide 1- 17
V
EHICLE WEIGHT PROBLEM 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.?
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I
S THIS STRONG EVIDENCE THAT THE MEAN WEIGHT OF ALL CARS IS NOT
3000
LBS
,
ASSUME A SIGNIFICANCE LEVEL OF
0.05?
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2.
3.
4.
Yes, there is sufficient evidence the mean is different from 3000 No, there is sufficient evidence the mean is different from 3000 Yes, there is NOT sufficient evidence the mean is different from 3000 No, there is NOT sufficient evidence the mean is different from 3000
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R
AT
P
ROBLEM
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0% 0% 0% 0%
T
EST THE HYPOTHESIS THAT THE MEAN COMPLETION TIME FOR THIS MAZE IS
60
SEC
.,
ASSUME A SIGNIFICANCE LEVEL OF
0.05.
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 1- 21
0% 0% 0% 0%
E
LIMINATE 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 1- 22
D
O YOU THINK
THIS
MAZE MEETS THE 1.
0%
“
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 meets the requirements.
2.
0%
There is evidence that the mean time required for rats to complete the maze is different from 60s. The maze meets the requirements.
3.
0%
There is evidence that the mean time required for rats to complete the maze is different from 60s. The maze DOES NOT meet the requirements.
4.
0%
There is NOT evidence that the mean time required for rats to complete the maze is different from 60s. The maze DOES NOT meet the requirements.
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U
PCOMING IN
C
LASS Homework #11 due Sunday Quiz #6 is next Wednesday Exam #2 is in two weeks Last week of class, work on data project.
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