Question

6.2.25 Rising mercury levels due to industrial pollution is a recent concern. Many fish have high levels of mercury. Data were collected on random samples of tuna from 1991 to 2010 and are available in the file Tuna. Each row in the data set represents the mercury level of a different fish. With randomization techniques we are able to analyze any test statistic we desire. What if we wanted to look at whether there was a difference in the median values of mercury in the Yellowfin tuna compared to the Albacore tuna? Use the Multiple Means applet with the Median option to answer the following questions.

Is this an experiment or an observational study? Explain how you know.

Observational study: Researchers did not assign variable values to the fish.

Experiment: Researchers assigned variable values to the fish.

Identify the observational units.

Levels of mercury

Each fish

The years 1991 to 2010

The two types of tuna

Identify the explanatory and response variable. Also, identify whether each is quantitative or categorical.

Explanatory: mercury level (quantitative), response: type of tuna (categorical)

Explanatory: type of tuna (categorical), response: mercury level (quantitative)

Explanatory: mercury level (categorical), response: type of tuna (quantitative)

Explanatory: type of tuna (quantitative), response: mercury level (categorical)

Define (in words) the parameters of interest of this study.

The median mercury level in albacore tuna;the median mercury level in yellowfin tuna

The number of albacore tuna; the number of yellowfin tuna

State the null and alternative hypotheses in words.

Null: The median mercury level in albacore tuna is the same as in yellowfin tuna Alt: The median mercury level in albacore tuna is different from that in yellowfin tuna.

Null: The median mercury level in albacore tuna is greater than in yellowfin tuna. Alt: The median mercury level in albacore tuna is the same as in yellowfin tuna.

Null: The median mercury level in albacore tuna is different from that in yellowfin tuna. Alt: The median mercury level in albacore tuna is the same as in yellowfin tuna.

Null: The median mercury level in albacore tuna is the same as in yellowfin tuna Alt: The median mercury level in albacore tuna is greater than in yellowfin tuna.

What statistic will you use?

Difference of sample means

Difference in sample medians

Use an appropriate applet to carry out a simulation analysis. Report the p-value. the absolute tolerance is +/-0.02 Use the 2SD rule to determine a 95% confidence interval. ( , )

Answer 1