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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 0.05 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 81 75 52 79 77 34 40 87 64 39 32 72 47 43 61 58 57 47 48 46

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 0.05 level of significance. Sunscreen A Sunscreen B Sunscreen C Sunscreen D 81 75 52 79 77 34 40 87 64 39 32 72 47 43 61 58 57 47 48 46

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 2CYU
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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 0.05 level of significance.

Sunscreen A Sunscreen B Sunscreen C Sunscreen D
81 75 52 79
77 34 40 87
64 39 32 72
47 43 61 58
57 47 48 46
80 43 38 63

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=0.05α=0.05 

 

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:

  • reject H0H0
  • do not reject H0H0

The final conclusion is:

  • There is not enough evidence to reject 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 support the claim that at least one sunscreen lasts a different amount of time.
  • There is enough evidence to reject the claim that at least one sunscreen lasts a different amount of time.
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