Question

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
51	69	37	79
44	36	52	55
89	48	66	62
64	72	61	81
48	32	48	59
63	66	35	80

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 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.

Answer 1

Solution:

We can use the excel data analysis tool to find the answers to the given questions. The excel output is given below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Sunscreen A	6	359	59.83333333	269.3666667
Sunscreen B	6	323	53.83333333	307.3666667
Sunscreen C	6	299	49.83333333	155.7666667
Sunscreen D	6	416	69.33333333	141.8666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1294.125	3	431.375	1.973428386	0.150449036	2.380087057
Within Groups	4371.833333	20	218.5916667
Total	5665.958333	23

The hypotheses for this ANOVA test would be:

HA: At least one mean is different. (claim)

Complete the ANOVA table below: (round answers to 3 decimal places)

Source of Variation	SS	df	MS	F	P-value
Between	1294.125	3	431.375	1.973	0.150
Within	4371.833	20	218.592

The decision of the test is to:

Answer: do not reject H0

The final conclusion is:

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