The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in a random sample of different lakes to measure the average amount of mercury in the sample of fish from each lake. The data for the average amount of mercury in each lake is in table below. Do the data provide enough evidence to show that the fish in all Florida lakes have a lower mercury level than the allowable amount? Test at the 3% level.mercury level of fish in mg/kg0.490.710.270.270.180.210.280.040.650.50.830.630.730.480.981.160.340.040.251.20.430.810.941.330.40.171.10.520.410.51.080.340.190.190.10.050.190.150.560.480.560.860.870.440.770.840.160.27P: Parameter What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: Hypotheses Fill in the correct null and alternative hypotheses:𝐻0: 1 mg/kg 𝐻𝐴: 1 mg/kg A: Assumptions Since information was collected from each object, what conditions do we need to check? Check all that apply. no outliers in the dataσσ is knownoutliers in the data𝑛(1-𝑝)≥10𝑁≥20𝑛𝑛≥30 or normal population𝑛𝑝≥10𝑛(1-𝑝̂)≥10σσ is unknown𝑛(𝑝̂)≥10 Check those assumptions: 1. Is the value of 𝜎 known? 2. Which of the following is the correct modified boxplot? 012mercury level of fish in mg/kg0.040.230.480.791.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.23,2],[0.79,4]); line([0.48,2],[0.48,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.23,3]); line([0.79,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.23,4],'0.23','above');text([0.48,4],'0.48','above');text([0.79,4],'0.79','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]012mercury level of fish in mg/kg0.040.1350.480.791.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.135,2],[0.79,4]); line([0.48,2],[0.48,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.135,3]); line([0.79,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.135,4],'0.135','above');text([0.48,4],'0.48','above');text([0.79,4],'0.79','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]012mercury level of fish in mg/kg0.040.230.481.061.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.23,2],[1.06,4]); line([0.48,2],[0.48,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.23,3]); line([1.06,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.23,4],'0.23','above');text([0.48,4],'0.48','above');text([1.06,4],'1.06','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]012mercury level of fish in mg/kg0.040.230.3550.791.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.23,2],[0.79,4]); line([0.355,2],[0.355,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.23,3]); line([0.79,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.23,4],'0.23','above');text([0.355,4],'0.355','above');text([0.79,4],'0.79','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;] Are there any outliers? 3. 𝑛 = which is Is it reasonable to assume the population is normally distributed? N: Name the test The conditions are met to use a .T: Test Statistic The symbol and value of the random variable on this problem are as follows: = mg/kg The test statistic formula set up with numbers is as follows: Round values to 4 decimal places. 𝑡=𝑋¯-𝜇𝑠𝑛=(( - ) / / )) The final answer for the test statistic from technology is as follows: Round to 2 decimal places. t = O: Obtain the P-value Report the final answer to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: Make a decision Since the p-value , we .S: State a conclustion There significant evidence to conclude mg/kg
Question
The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in a random sample of different lakes to measure the average amount of mercury in the sample of fish from each lake. The data for the average amount of mercury in each lake is in table below. Do the data provide enough evidence to show that the fish in all Florida lakes have a lower mercury level than the allowable amount? Test at the 3% level.mercury level of fish in mg/kg0.490.710.270.270.180.210.280.040.650.50.830.630.730.480.981.160.340.040.251.20.430.810.941.330.40.171.10.520.410.51.080.340.190.190.10.050.190.150.560.480.560.860.870.440.770.840.160.27P: Parameter What is the correct parameter symbol for this problem? What is the wording of the parameter in the context of this problem? H: Hypotheses Fill in the correct null and alternative hypotheses:𝐻0: 1 mg/kg 𝐻𝐴: 1 mg/kg A: Assumptions Since information was collected from each object, what conditions do we need to check? Check all that apply. no outliers in the dataσσ is knownoutliers in the data𝑛(1-𝑝)≥10𝑁≥20𝑛𝑛≥30 or normal population𝑛𝑝≥10𝑛(1-𝑝̂)≥10σσ is unknown𝑛(𝑝̂)≥10 Check those assumptions: 1. Is the value of 𝜎 known? 2. Which of the following is the correct modified boxplot? 012mercury level of fish in mg/kg0.040.230.480.791.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.23,2],[0.79,4]); line([0.48,2],[0.48,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.23,3]); line([0.79,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.23,4],'0.23','above');text([0.48,4],'0.48','above');text([0.79,4],'0.79','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]012mercury level of fish in mg/kg0.040.1350.480.791.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.135,2],[0.79,4]); line([0.48,2],[0.48,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.135,3]); line([0.79,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.135,4],'0.135','above');text([0.48,4],'0.48','above');text([0.79,4],'0.79','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]012mercury level of fish in mg/kg0.040.230.481.061.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.23,2],[1.06,4]); line([0.48,2],[0.48,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.23,3]); line([1.06,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.23,4],'0.23','above');text([0.48,4],'0.48','above');text([1.06,4],'1.06','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]012mercury level of fish in mg/kg0.040.230.3550.791.33[Graphs generated by this script: setBorder(15); initPicture(0,2,-3,6);axes(1,100,1,null,null,1,'off');text([0.645,-3],"mercury level of fish in mg/kg");line([0.04,2],[0.04,4]); rect([0.23,2],[0.79,4]); line([0.355,2],[0.355,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.23,3]); line([0.79,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.23,4],'0.23','above');text([0.355,4],'0.355','above');text([0.79,4],'0.79','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;] Are there any outliers? 3. 𝑛 = which is Is it reasonable to assume the population is normally distributed? N: Name the test The conditions are met to use a .T: Test Statistic The symbol and value of the random variable on this problem are as follows: = mg/kg The test statistic formula set up with numbers is as follows: Round values to 4 decimal places. 𝑡=𝑋¯-𝜇𝑠𝑛=(( - ) / / )) The final answer for the test statistic from technology is as follows: Round to 2 decimal places. t = O: Obtain the P-value Report the final answer to 4 decimal places. It is possible when rounded that a p-value is 0.0000 P-value = M: Make a decision Since the p-value , we .S: State a conclustion There significant evidence to conclude mg/kg
Solution
P: Parameter The correct parameter symbol for this problem is μ (mu), which represents the population mean. The wording of the parameter in the context of this problem is "the average mercury level in fish from all Florida lakes".
H: Hypotheses The null hypothesis (H0) is that the average mercury level in fish from all Florida lakes is equal to the FDA allowable amount, i.e., μ = 1 mg/kg. The alternative hypothesis (HA) is that the average mercury level is less than the FDA allowable amount, i.e., μ < 1 mg/kg.
A: Assumptions The conditions we need to check are: no outliers in the data, the sample size is large enough (n≥30), and the population is normally distributed.
- The value of σ (standard deviation) is unknown.
- To determine the correct modified boxplot, we need to calculate the quartiles of the data and identify any potential outliers. Without the actual data or the calculated quartiles, it's impossible to choose the correct boxplot.
- To check for outliers, we need to calculate the interquartile range (IQR) and identify any data points that fall below Q1 - 1.5IQR or above Q3 + 1.5IQR.
- The sample size (n) is not provided in the problem, so we cannot determine if it's large enough.
- Without the raw data or a provided histogram, we cannot determine if it's reasonable to assume the population is normally distributed.
N: Name the test Without knowing the sample size and the population standard deviation, we cannot definitively name the test. However, if the sample size is large enough and the population is normally distributed, we could use a one-sample t-test.
T: Test Statistic The test statistic formula is t = (X̄ - μ) / (s / √n), where X̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. Without these values, we cannot calculate the test statistic.
O: Obtain the P-value Without the test statistic, we cannot calculate the p-value.
M: Make a decision Without the p-value, we cannot make a decision about the null hypothesis.
S: State a conclusion Without making a decision about the null hypothesis, we cannot state a conclusion about the average mercury level in fish from all Florida lakes.
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