Question

The Food and Drug Administration advises people against eating fish with mercury concentrations exceeding 1 part per million (ppm). Researchers wonder if the average mercury content of large-mouth bass in a certain state exceeds the limits and, thus, make such fish inedible.

They randomly sample large-mouth bass from randomly selected lakes in this state and record the amount of mercury in each fish. A p-value of 0.005 was obtained from a hypothesis test. Which of the following is a correct conclusion based on this p-value?

There is not enough evidence to indicate the average mercury content of largemouth bass in this certain state exceeds 1 part per million.

There is some evidence to indicate the average mercury content of largemouth bass in this certain state exceeds 1 part per million.

There is not enough evidence to indicate the average mercury content of largemouth bass in this certain state is 1 part per million.

There is strong evidence to indicate the average mercury content of largemouth bass in this certain state is 1 part per million.

There is strong evidence to indicate the average mercury content of largemouth bass in this certain state exceeds 1 part per million.

Sulfur dioxide affects human health when it is breathed in by irritating the nose, throat, and airways to cause coughing, wheezing, shortness of breath, or a tight feeling around the chest. The effects of sulfur dioxide are felt very quickly and most people would feel the worst symptoms in 10 or 15 minutes after breathing it in. Those most at risk of developing problems if they are exposed to sulfur dioxide are people with asthma or similar conditions (Australian Government, Sulfur dioxide (SO2) (Links to an external site.)Links to an external site.).

The United States Environmental Protection Agency has set a standard that sulfur dioxide (SO2) should not exceed 75 parts per billion (PPB) over a one-hour period. Fortunately, the United States has done a good job at reducing sulfur dioxide in the atmosphere.

To determine if the average SO2 of cities in the United States is less than 75 ppb, a random sample of 41 cities in the United States was taken. The average SO2 levels of the 41 cities was = 30.5 ppb.

(Note: the data used in this example is a bit old. SO2 levels have actually decreased more since these data were collected!)

What is the variable of interest?

whether or not a city has SO2 levels below 75 ppb

SO2 level

whether or not SO2 levels have decreased over time

cities in the United States

the number of cities in the sample

Answer 1

For the research

Null hypothesis : average mercury content of large-mouth bass is 1 part per million (ppm)

Alternate hypothesis : average mercury content of large-mouth bass is more than 1 part per million (ppm)

p value : 0.005

Critical p value at 1% level of significance = 0.01

Since, p value < p sig, we reject Null hypothesis

That mean alternate is accepted.

Or, average mercury content of large-mouth bass is more than 1 part per million (ppm)

or part 5 is most appropriate , that is :

There is strong evidence to indicate the average mercury content of large mouth bass in this certain state exceeds 1 part per million.

Why strong ? Because even at the 1% level of significance the result shows that the content of large mouth bass in this certain state exceeds 1 part per million

Null Hypothesis : sulfur dioxide (SO2) have 75 parts per billion (PPB) over a one-hour period

mean = 75 parts per billion (PPB) over a one-hour period

Alternate Hypothesis :  sulfur dioxide (SO2) is less than 75 parts per billion (PPB) over a one-hour period

So, the variable of interest becomes SO2 level

Why? we will try to control the value of SO2 level in null hypothesis and proceed the test