OUR ANSWERS

The hypotheses are

$H_{0}$ : $μ_{1} = μ_{2} = μ_{3}$

$H_{a}$ : the $μ$ s are not all equal (Alternatively, at least one mean is different.)

Where:

$μ_{1} =$ mean CFF of people that have brown eyes.

$μ_{2} =$ mean CFF of people that have green eyes.

$μ_{3} =$ mean CFF of people that have blue eyes.
We can also state the null hypothesis as there is no relationship between eye color and Critical Flicker Frequency (CFF) threshold, and the alternative hypothesis as there is a relationship between eye color and CFF.
Here are our StatCrunch output screens:

Summary statistics for CFF:
Group by: Color

Color n Mean Std. dev.

Blue 6 28.166667 1.5279616

Brown 8 25.5875 1.3653231

Green 5 26.92 1.8430952

Let's check the conditions:
1. We are told that the sample was chosen at random, so the three eye-color samples are independent.
2. The sample sizes are small, but the boxplots do not show extreme skewness or outliers. Therefore, we assume that the distributions of CFF in the three eye-color populations are normal in shape.
3. We can also assume that the population standard deviations are equal because the rule of thumb is satisfied (1.843 / 1.365 is less than 2).
  
  In summary, we can safely proceed with the ANOVA F-test.
Since the first two columns are the stacked data format and the last three columns are the unstacked format, you could use either method to carry out the ANOVA F-test. We used the stacked data format.

Analysis of Variance results:
Responses: CFF
Factors: Color

Response statistics by factor

Color n Mean Std. Dev. Std. Error

Blue 6 28.166667 1.5279616 0.62378771

Brown 8 25.5875 1.3653231 0.48271461

Green 5 26.92 1.8430952 0.82425724

ANOVA table

Source DF SS MS F-Stat P-value

Color 2 22.997285 11.498643 4.8023461 0.0232

Error 16 38.310083 2.3943802

Total 18 61.307368

The test statistic F is 4.8 (which is quite large), and the P-value is 0.023, which is less than 0.05 level of significance.

The small P-value indicates that it is unlikely (probability of 0.023) to get data with larger sample differences than those observed assuming that CFF is not related to eye color (as the null hypothesis claims).
Conclusion: We have enough evidence in the data to reject H₀ and conclude that the mean CFFs in the three eye-color populations are not all the same. In other words, we can conclude that CFF is related to eye color.