USE EXCEL Healthy Snacks decides to change its pretzels supplier. In the review
ID: 3371721 • Letter: U
Question
USE EXCEL Healthy Snacks decides to change its pretzels supplier. In the review process, they limit their options to four suppliers. Except Sodium level, every other specification of pretzels produced by the four suppliers is the same. Table below lists the sodium level in pretzels obtained by sampling the products of each supplier.
No. Supplier 1 Supplier 2 Supplier 3 Supplier 4 1 2.93 3.09 3.38 3.36 2 3.18 2.73 3.03 3.34 3 3.05 2.70 2.53 3.68 4 3.34 2.91 2.58 3.70 5 2.68 2.82 2.67 3.33 6 2.92 2.68 2.54 3.42 7 2.91 3.03 2.71 3.45 8 2.63 2.96 2.79 3.25 9 2.90 2.84 2.51 3.42 10 3.28 2.37 3.26 3.75 11 2.55 2.44 2.58 2.98 12 3.15 2.78 3.11 3.12 13 3.09 2.86 2.53 3.35 14 2.94 2.28 2.44 3.72 15 2.84 2.72 2.79 2.93 ? 0.05Explanation / Answer
One-way ANOVA: Response versus Supplier
Source DF SS MS F P
Supplier 3 3.9882 1.3294 20.53 0.000
Error 56 3.6255 0.0647
Total 59 7.6137
Since p-value=0.000<0.05 we conclude that there is a significant difference between the sodium level of pretzels produced by each supplier.
Individual 95% CIs For Mean Based on
Pooled StDev
Level N Mean StDev -----+---------+---------+---------+----
Supplier 1 15 2.9593 0.2291 (----*-----)
Supplier 2 15 2.7473 0.2329 (----*----)
Supplier 3 15 2.7633 0.2959 (-----*----)
Supplier 4 15 3.3867 0.2542 (----*-----)
-----+---------+---------+---------+----
2.75 3.00 3.25 3.50
Pooled StDev = 0.2544
Grouping Information Using Tukey Method
Supplier N Mean Grouping
Supplier 4 15 3.3867 A
Supplier 1 15 2.9593 B
Supplier 3 15 2.7633 B
Supplier 2 15 2.7473 B
Means that do not share a letter are significantly different.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of Supplier
Individual confidence level = 98.94%
Supplier = Supplier 1 subtracted from:
Supplier Lower Center Upper --------+---------+---------+---------+-
Supplier 2 -0.4577 -0.2120 0.0337 (----*----)
Supplier 3 -0.4417 -0.1960 0.0497 (----*----)
Supplier 4 0.1816 0.4273 0.6730 (----*---)
--------+---------+---------+---------+-
-0.50 0.00 0.50 1.00
Supplier = Supplier 2 subtracted from:
Supplier Lower Center Upper --------+---------+---------+---------+-
Supplier 3 -0.2297 0.0160 0.2617 (----*----)
Supplier 4 0.3936 0.6393 0.8850 (----*----)
--------+---------+---------+---------+-
-0.50 0.00 0.50 1.00
Supplier = Supplier 3 subtracted from:
Supplier Lower Center Upper --------+---------+---------+---------+-
Supplier 4 0.3776 0.6233 0.8690 (---*----)
--------+---------+---------+---------+-
-0.50 0.00 0.50 1.00
From the Tukey's HSD, we see that C.I.s of the differences (Supplier 1-Supplier 4), (Supplier 2-Supplier 4), (Supplier 3-Supplier 4) donot contain zero so Supplier 4 is significantly different from others. Since average sodium level in pretzels is maximum in Supplier 4, so we can pick any one of Supplier1-Supplier 3 in order to minimize the cost of one bag of snack.
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