In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?
Brand | ||
x | y | z |
91 | 99 | 83 |
100 | 96 | 88 |
88 | 94 | 89 |
89 | 99 | 76 |
Check whether there is a significant difference among the mean absorbency ratings for the three brands at
Answer to Problem 34SE
Yes, there appear to be a difference in the ability of the brands to absorb water.
Explanation of Solution
Calculation:
The data represents the absorbency rate for the three brands.
State the hypotheses:
Null hypothesis:
Alternative hypothesis:
The level of significance is 0.05.
Software procedure:
Step by step procedure to obtain One-Way ANOVA using the MINITAB software:
- Choose Stat > ANOVA > One-Way.
- In Response, enter the column of values.
- In Factor, enter the column of Brands.
- Click OK.
Output using the MINITAB software is given below:
From the Minitab output the F-ratio is 7.23 and the p-value is 0.0134.
Decision:
If
If
Conclusion:
Here, the p-value is less than the level of significance.
That is,
Therefore, the null hypothesis is rejected.
Hence, there is sufficient evidence to infer that there is a significant difference among the mean absorbency ratings for the three brands at
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Chapter 13 Solutions
STATISTICS F/BUSINESS+ECONOMICS-TEXT
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt