A sunscreen company is attempting to improve upon their formula so that it lasts in water longer. They have 4 lead scientists who each came up with a different formulas. In order to see if there is a difference in the time the sunscreen lasts the CEO collects a random sample of each of the four sunscreens the data is shown below. Test the claim that at least one sunscreen has a different lifespan in water at a 0.10 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 66 68 57 73 73 55 65 53 48 45 44 77 52 38 42 62 40 72 62 69 65 32 66 48 The hypotheses for this ANOVA test would be: H0:μA=μB=μC=μDH0:μA=μB=μC=μD HA:HA: At least one mean is different. (claim) α=0.10α=0.10 Complete the ANOVA table below: (round answers to 3 decimal places) SS df MS F p-value Between Within The decision of the test is to: do not reject H0H0 reject H0H0 The final conclusion is: There is enough evidence to reject the claim that at least one sunscreen lasts a different amount of time. There is not enough evidence to support the claim that at least one sunscreen lasts a different amount of time. There is enough evidence to support the claim that at least one sunscreen lasts a different amount of time. There is not enough evidence to reject the claim that at least one sunscreen lasts a different amount of time.
A sunscreen company is attempting to improve upon their formula so that it lasts in water longer. They have 4 lead scientists who each came up with a different formulas. In order to see if there is a difference in the time the sunscreen lasts the CEO collects a random sample of each of the four sunscreens the data is shown below. Test the claim that at least one sunscreen has a different lifespan in water at a 0.10 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 66 68 57 73 73 55 65 53 48 45 44 77 52 38 42 62 40 72 62 69 65 32 66 48 The hypotheses for this ANOVA test would be: H0:μA=μB=μC=μDH0:μA=μB=μC=μD HA:HA: At least one mean is different. (claim) α=0.10α=0.10 Complete the ANOVA table below: (round answers to 3 decimal places) SS df MS F p-value Between Within The decision of the test is to: do not reject H0H0 reject H0H0 The final conclusion is: There is enough evidence to reject the claim that at least one sunscreen lasts a different amount of time. There is not enough evidence to support the claim that at least one sunscreen lasts a different amount of time. There is enough evidence to support the claim that at least one sunscreen lasts a different amount of time. There is not enough evidence to reject the claim that at least one sunscreen lasts a different amount of time.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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A sunscreen company is attempting to improve upon their formula so that it lasts in water longer. They have 4 lead scientists who each came up with a different formulas. In order to see if there is a difference in the time the sunscreen lasts the CEO collects a random sample of each of the four sunscreens the data is shown below. Test the claim that at least one sunscreen has a different lifespan in water at a 0.10 level of significance.
| Sunscreen A | Sunscreen B | Sunscreen C | Sunscreen D |
| 66 | 68 | 57 | 73 |
| 73 | 55 | 65 | 53 |
| 48 | 45 | 44 | 77 |
| 52 | 38 | 42 | 62 |
| 40 | 72 | 62 | 69 |
| 65 | 32 | 66 | 48 |
The hypotheses for this ANOVA test would be:
H0:μA=μB=μC=μDH0:μA=μB=μC=μD
HA:HA: At least one mean is different. (claim)
α=0.10α=0.10
Complete the ANOVA table below: (round answers to 3 decimal places)
| SS | df | MS | F | p-value | |
| Between | |||||
| Within |
The decision of the test is to:
- do not reject H0H0
- reject H0H0
The final conclusion is:
- There is enough evidence to reject the claim that at least one sunscreen lasts a different amount of time.
- There is not enough evidence to support the claim that at least one sunscreen lasts a different amount of time.
- There is enough evidence to support the claim that at least one sunscreen lasts a different amount of time.
- There is not enough evidence to reject the claim that at least one sunscreen lasts a different amount of time.
Expert Solution
Step 1
State the hypotheses:
H0:μA=μB=μC=μD
HA: At least one mean is different. (claim)
The level of significance is 0.05.
Procedure to obtain One-Way ANOVA using the EXCEL:
- Go to Data -> Data Analysis.
- Select “Anova: Single Factor” from Analysis Tool.
- Select the columns “Sunscreen A”, “Sunscreen B”, “Sunscreen C” and “Sunscreen D” in Input range and click Ok.
Output:
From the output the F-ratio is 0.891.
P-value:
From the output, the P-value is 0.463.
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