DID YOU VOTE?
1.
2.
3.
Yes
No
I’ll get to it.
29%
29%
14%
14%
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0%
1
14%
2
3
4
5
6
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
y t

n 1
 SE  y 
where the standard error of the mean is
s
SE  y  
n
*
 The critical value tn 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.
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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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
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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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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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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.
DATA – CREATE A 95% CI
1022
1142
1120
1269
1276
1228
1202
1317
1325
1491
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IS THE DATA NEARLY NORMAL?
1.
2.
Yes
No
100%
0%
1
2
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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
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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.?

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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.
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HW 11 -PROBLEM 11
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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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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.
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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.
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UPCOMING IN CLASS

Homework #11 due Sunday

Quiz #4 is Wednesday November 14th

Exam #2 is Wednesday November 28th

Last week of class, work on data project.
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