Problem: Cestomers are complaining about sandwich leagth You are the owner of three local sondwich shops. Recently you've received complaints from customers that their "footlong" sub sandwiches were less than 12 inches long. As a measure of quolity acsurance, data was collected on all footlong sub sondwiches made over the period of an hour at cach store. Determined which, if any, of your stores are making sub sondwiches that are significantly shorter than 12 inches. You will conduct three t-tests, one for cach store. You want to be 95% confident in your reculto. (Note. This case ic inspired by reality. Scarch the internet for "claims over footlong sub' for a historical perspective and how a company used statistics to incure consistent quality.) Sandwich Measurements Store 1 Store 2 Store 3 Statistics Store 1 Store 2 Store 3 8.8 9.1 9.0 Somple Size Mean (length) 11.4 11.6 12.5 13.4 13.4 15.1 Variance 11.3 11.4 14.3 Standard Deviation 10.1 10.3 10.8 12.4 12.4 13.8 Hypothesised Meon (M) Difference in Means (2 - M) 10.4 10.6 11.2 8.9 3.2

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Problem: Customers are complaining about sandwich leagth
You are the owner of three local sandwich shops. Recently you've received complaints from
customers that their "footlong" sub sandwiches were les than 12 inches long. As a measure of
1
quality assurance, data was collected on all footlong sub sondwiches made over the pcriod of an
hour at cach store. Determined which, if any, of your stores are making sub sandwiches that are
significantly shorter than 12 inches. You will conduct three t-tests, one for coch store. You want
4
6.
to be 95% confident in your recults. (Note. This case is inspired by reality. Scarch the internet for
"claims over footlong sub' for a historical perspective and how a company used statistics to
incure consistent quality.)
17
10
11 SandwicL Measuremeat:
12 Store 1 Store 2 Store 3
Statistics
Store 1 Store 2 Store 3
13
8.8
3.1
9.0
Somple Size
Mean (length)
14
11.4
11.6
12.5
15
13.4
13.4
15.1
Variance
Standard Deviation
16
11.3
11.4
14.3
17
10.1
10.3
10.8
18
12.4
12.4
Hypothesized Mean (M)
Difference in Means (X - M)
Stondard Error
13.8
19
10.4
10.6
11.2
20
8.9
9.2
3.1
21
10.4
11.1
T-Statistic
22
11.8
14.0
Degrees of Frcedom
23
12.8
14.3
24
9.3
8.7
P-value P(T=t) two-tail
25
12.6
13.7
"Remomberthat the T.DIST.2T) Function requiror the t-
statirkic arqumont ta be an abralute value, nat a noqativo value,
26
11.7
12.9
27
11.8
13.0
or an orror uill occur.
28
3.7
10.2
29
12.6
14.1
30
8.6
Interpret the Reselts
8.6
1. What is the null hypothesis for these teste?
2. What is the alternative hypothesis for these teste?
3. Given the desired confidence level, whst alpha should be used?
4. Can you say with 95% confidence that Store 1 is producing sub
31
14.6
[select]
[select]
32
11.0
33
[select]
34
candwiches with an average length that is less than 12 inchcs?
5. Can you say with 95% confidence that Store 2 is producing sub
35
[select]
36
sandwiches with an average length that is less than 12 inches?
6. Con you say with 95% confidence that Store 3 is producing sub
condwiches with an average length that is less than 12 inches?
37
[sclect]
38
39
[sclect]
Glossary
Case 1
Case 2
Sandwich Shop
Ready
P Type here to search
耳|
Transcribed Image Text:Alignment Font Clipboard fe L2 E G. H. K A. C D Problem: Customers are complaining about sandwich leagth You are the owner of three local sandwich shops. Recently you've received complaints from customers that their "footlong" sub sandwiches were les than 12 inches long. As a measure of 1 quality assurance, data was collected on all footlong sub sondwiches made over the pcriod of an hour at cach store. Determined which, if any, of your stores are making sub sandwiches that are significantly shorter than 12 inches. You will conduct three t-tests, one for coch store. You want 4 6. to be 95% confident in your recults. (Note. This case is inspired by reality. Scarch the internet for "claims over footlong sub' for a historical perspective and how a company used statistics to incure consistent quality.) 17 10 11 SandwicL Measuremeat: 12 Store 1 Store 2 Store 3 Statistics Store 1 Store 2 Store 3 13 8.8 3.1 9.0 Somple Size Mean (length) 14 11.4 11.6 12.5 15 13.4 13.4 15.1 Variance Standard Deviation 16 11.3 11.4 14.3 17 10.1 10.3 10.8 18 12.4 12.4 Hypothesized Mean (M) Difference in Means (X - M) Stondard Error 13.8 19 10.4 10.6 11.2 20 8.9 9.2 3.1 21 10.4 11.1 T-Statistic 22 11.8 14.0 Degrees of Frcedom 23 12.8 14.3 24 9.3 8.7 P-value P(T=t) two-tail 25 12.6 13.7 "Remomberthat the T.DIST.2T) Function requiror the t- statirkic arqumont ta be an abralute value, nat a noqativo value, 26 11.7 12.9 27 11.8 13.0 or an orror uill occur. 28 3.7 10.2 29 12.6 14.1 30 8.6 Interpret the Reselts 8.6 1. What is the null hypothesis for these teste? 2. What is the alternative hypothesis for these teste? 3. Given the desired confidence level, whst alpha should be used? 4. Can you say with 95% confidence that Store 1 is producing sub 31 14.6 [select] [select] 32 11.0 33 [select] 34 candwiches with an average length that is less than 12 inchcs? 5. Can you say with 95% confidence that Store 2 is producing sub 35 [select] 36 sandwiches with an average length that is less than 12 inches? 6. Con you say with 95% confidence that Store 3 is producing sub condwiches with an average length that is less than 12 inches? 37 [sclect] 38 39 [sclect] Glossary Case 1 Case 2 Sandwich Shop Ready P Type here to search 耳|
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