12.4 ## Arsenic Levels in Brown Rice from Different StatesThe following analysis examines the arsenic amounts in brown rice samples collected from three states: Arkansas, California, and Texas. The amounts are measured in micrograms, with each sample maintaining a consistent serving size. Data is provided by the Food and Drug Administration.### Hypothesis TestingWe aim to determine if the arsenic levels differ significantly across these states using a 0.05 significance level. Specifically, we want to ascertain whether brown rice from Texas, which shows the highest arsenic average, poses a greater health risk.**Hypotheses:**- **Null Hypothesis (H₀):** μ₁ = μ₂ = μ₃- **Alternative Hypothesis (H₁):** At least one of the means is different from the others### Arsenic Amounts by State#### Arkansas:- Data points: 4.77, 4.92, 5.03, 5.39, 5.38, 5.39, 5.56, 5.62, 5.58, 5.92, 6.04, 6.14#### California:- Data points: 1.50, 3.66, 4.00, 4.49, 4.88, 5.12, 5.32, 5.38, 5.39, 5.45, 5.63, 5.62#### Texas:- Data points: 5.57, 5.81, 6.57, 6.91, 6.92, 6.85, 7.06, 7.28, 7.48, 7.58, 7.73, 7.70### Next Steps1. Calculate the test statistic using the data provided.2. Round the test statistic to two decimal places.The outcome of this test will help determine if the arsenic levels in Texas rice are significantly higher than those in Arkansas and California, bearing implications for public health safety. **Determine the P-value:**The P-value is ___.(Round to three decimal places as needed.)**Do the amounts of arsenic appear to be different in the different states?**There ___ sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the three different states have ___ mean arsenic content(s) in brown rice.**Given that the amounts of arsenic in the samples from Texas have the highest mean, can we conclude that brown rice from Texas poses the greatest health problem?**- **A.** The results from ANOVA do not allow us to conclude that any one specific population mean is different from the others, so we cannot conclude that brown rice from Texas poses the greatest health problem.- **B.** The results from ANOVA allow us to conclude that Texas has the highest population mean, so we can conclude that brown rice from Texas poses the greatest health problem.- **C.** Although the amounts of arsenic in the samples from Texas have the highest mean, there may be other states that have a higher mean, so we cannot conclude that brown rice from Texas poses the greatest health problem.- **D.** Because the amounts of arsenic in the samples from Texas have the highest mean, we can conclude that brown rice from Texas poses the greatest health problem.

ArkansasCaliforniaTexas4.771.55.574.923.665.815.0346.575.394.496.915.384.886.925.395.126.855.565.327.065.625.387.285.585.397.485.925.457.586.045.637.736.145.627.7Use the given data to form the table:ArkansasCaliforniaTexas4.771.55.574.923.665.815.0346.575.394.496.915.384.886.925.395.126.855.565.327.065.625.387.285.585.397.485.925.457.586.045.637.736.145.627.7Sum65.7456.4483.46Average5.4783333334.7033333336.9552.02516666715.661066675.3303ANOVASource of VariationSSdfMSFP-valueBetween Groups31.40468889215.7023422.513270.0000Within Groups23.01653333330.697471Total54.4212222235Null hypothesis: Alternative hypothesis: HA : At-least one of the is not equal. For this analysis, the significance level is 0.05. F statistics is given by:- Use the excel formula, "=F.DIST.RT(22.51,2,33)" to determine the P-value: The P-value = 0.0000Since the P-value (0.0000) is less than the significance level (0.05), we have to reject the null hypothesis.Conclusion:-There is sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the three different states have same mean arsenic content(s) in brown rice.A) The results from ANOVA do not allow us to conclude that any one specific population mean is different from the others, so we cannot conclude that brown rice from Texas poses the greatest health problem. ANOVA table:ANOVASource of VariationSSdfMSFP-valueBetween Groups31.40468889215.7023422.513270.0000Within Groups23.01653333330.697471Total54.4212222235Null hypothesis: Alternative hypothesis: HA : At-least one of the is not equal. For this analysis, the significance level is 0.05. F statistics is given by:- F = 22.51Use the excel formula, "=F.DIST.RT(22.51,2,33)" to determine the P-value: The P-value = 0.0000Since the P-value (0.0000) is less than the significance level (0.05), we have to reject the null hypothesis.Conclusion:-There is sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the three different states have same mean arsenic content(s) in brown rice.A) The results from ANOVA do not allow us to conclude that any one specific population mean is different from the others, so we cannot conclude that brown rice from Texas poses the greatest health problem.

Math

Statistics

The accompanying table gives 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. Do the amounts of arsenic appear to be different in the different states? Given that the amounts of arsenic in the samples from Texas have the highest mean, can we conclude that brown rice from Texas poses the greatest health problem? Click the icon to view the data. What are the hypotheses for this test? OA. Ho: H₁ H₁: H₁ OB. Ho: H₁ H₂=H3 H₂ #H3 H₂ #H3 H₁ H₁ H₂ H3 OC. Ho: At least one of the means is different from the others H₁ H₁ H₂=H3 D. Ho: H₁ H₂=H3 H₁: At least one of the means is different from the others Determine the test statistic. The test statistic is (Round to two decimal places as needed.) Arsenic Amounts Arkansas California Texas 4.77 4.92 5.03 5.39 5.38 5.39 5.56 5.62 5.58 5.92 6.04 6.14 1.50 3.66 4.00 4.49 4.88 5.12 5.32 5.38 5.39 5.45 5.63 5.62 5.57 5.81 6.57 6.91 6.92 6.85 7.06 7.28 7.48 7.58 7.73 7.70 Print Done X