Listed below are amounts of arsenic in samples of brown rice from three different states. The amounts are in micrograms of arsenic and all samples have the same serving size. The data are from the Food and Drug Administration. Use a 0.05 significance level to test the claim that the three samples are from populations with the same mean. Assume that the distributions for each state are normal and that all variances are equal.

Arkansas 4.8 4.9 5.0 5.4 5.4 5.4 5.6 5.6 5.6 5.9 6.0 6.1
California. 1.5 3.7 4.0 4.5 4.9 5.1 5.3 5.4 5.4 5.5 5.6 5.6
Texas. 5.6 5.8 6.6 6.9. 6.9 6.9 7.1 7.3 7.5 7.6 7.7 7.7

No, the claim that the three samples are from populations with the same mean is not correct and this can be determined by using the given data.

Given :

The amounts are in micrograms of arsenic and all samples have the same serving size.
The data are from the Food and Drug Administration.
Use a 0.05 significance level.

The Hypothesis test is given below:

Null Hypothesis: [tex]H_0:\mu_1=\mu_2=\mu_3[/tex]

Alternative Hypothesis: [tex]H_a:\mu_1\neq \mu_2\neq \mu_3[/tex]

For the F-test, the test statistics is given by:

[tex]F = \dfrac{MS_{\rm{between}}}{MS_{\rm{within}}}[/tex]

Now, substitute the values of known terms in the above expression.

[tex]F = \dfrac{15.8252}{0.6896}[/tex]

[tex]F = 22.95[/tex]

So, the p-value regarding the value of F is:

[tex]P-value=P(F>22.95)[/tex]

[tex]P-value = 1.0.9999[/tex]

[tex]P-value = 0.0001[/tex]

The Null Hypothesis is rejected because P-value is less than the significance value.

For more information, refer to the link given below:

https://brainly.com/question/10758924