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/kg 0.27 0.18 0.86 0.25 0.34 0.73 0.49 0.49 0.43 0.56 0.56 0.41 0.34 0.71 0.48 1.23 0.19 0.77 1.1 0.87 0.81 0.65 0.28 0.5 0.27 0.84 0.63 0.15 0.4 0.1 0.27 0.04 1.08 0.59 1.33 0.04 1.16 0.17 P: 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:H0: mg/kg HA:HA: mg/kg A: Assumptions Since information was collected from each object, what conditions do we need to check? Check all that apply. σσ is known outliers in the data np≥10np≥10 N≥20nN≥20n n(pˆ)≥10n(p̂)≥10 n(1−pˆ)≥10n(1-p̂)≥10 n(1−p)≥10n(1-p)≥10 n≥30n≥30 or normal population σσ is unknown no outliers in the data Check those assumptions: 1. Is the value of σσ known? 2. Given the following modified boxplot (If using a screenreader, use technology to generate the modified boxplot and answer the question below.): 012mercury level of fish in mg/kg0.040.270.490.771.33[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([0.27,2],[0.77,4]); line([0.49,2],[0.49,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.27,3]); line([0.77,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.27,4],'0.27','above');text([0.49,4],'0.49','above');text([0.77,4],'0.77','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;] Are there any outliers? 3. nn = which is Is it reasonable to assume the population is normally distributed?
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/kg |
|---|
| 0.27 |
| 0.18 |
| 0.86 |
| 0.25 |
| 0.34 |
| 0.73 |
| 0.49 |
| 0.49 |
| 0.43 |
| 0.56 |
| 0.56 |
| 0.41 |
| 0.34 |
| 0.71 |
| 0.48 |
| 1.23 |
| 0.19 |
| 0.77 |
| 1.1 |
| 0.87 |
| 0.81 |
| 0.65 |
| 0.28 |
| 0.5 |
| 0.27 |
| 0.84 |
| 0.63 |
| 0.15 |
| 0.4 |
| 0.1 |
| 0.27 |
| 0.04 |
| 1.08 |
| 0.59 |
| 1.33 |
| 0.04 |
| 1.16 |
| 0.17 |
P: 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:H0: mg/kg
HA:HA: mg/kg
A: Assumptions
Since information was collected from each object, what conditions do we need to check?
Check all that apply.
- σσ is known
- outliers in the data
- np≥10np≥10
- N≥20nN≥20n
- n(pˆ)≥10n(p̂)≥10
- n(1−pˆ)≥10n(1-p̂)≥10
- n(1−p)≥10n(1-p)≥10
- n≥30n≥30 or normal population
- σσ is unknown
- no outliers in the data
Check those assumptions:
1. Is the value of σσ known?
2. Given the following modified boxplot (If using a screenreader, use technology to generate the modified boxplot and answer the question below.):
012mercury level of fish in mg/kg0.040.270.490.771.33[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([0.27,2],[0.77,4]); line([0.49,2],[0.49,4]);line([1.33,2],[1.33,4]); line([0.04,3],[0.27,3]); line([0.77,3],[1.33,3]);fontsize*=.8;fontfill='blue';text([0.04,4],'0.04','above');text([0.27,4],'0.27','above');text([0.49,4],'0.49','above');text([0.77,4],'0.77','above');text([1.33,4],'1.33','above');fontfill='black';fontsize*=1.25;]
Are there any outliers?
3. nn = which is
Is it reasonable to assume the population is
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−μs√n=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
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
