Exercise 4 accuracy and precision

Exercise 1: Data Interpretation (2 pts each)

1. What patterns do you observe based on the information in Table 4?

No fish are present when the dissolved oxygen is zero. When there is more dissolved oxygen in the water, more fish are present. However, the number of fish tends to drop or level off when the dissolved oxygen is higher than 12 ppm.

2. Develop a hypothesis relating to the amount of dissolved oxygen measured in the water sample and the number of fish observed in the body of water.

Possible Hypotheses:

1. The amount of dissolved oxygen affects the number of fish that can live in a body of water.

2. As dissolved oxygen concentration increases, more fish can live in the body of water.

3. There is an ideal dissolved oxygen concentration for fish to live in.

3. What would your experimental approach be to test this hypothesis?

Possible Experimental Approach: Deposit an equal number of fish in several tanks. Maintain all other variables (temperature, light, food, etc.), but vary the dissolved oxygen concentration in each of the tanks. Observe the fish over time to determine how many fish can survive at different oxygen concentrations.

4. What are the independent and dependent variables?

Independent Variable: Dissolved oxygen concentration.

Dependent Variable: The number of fish.

5. What would be your control?

Possible Control: Aquarium with no fish. Measure the dissolved oxygen level in a fish tank at normal room conditions, and repeat this measurement every time you make an observation of the number of fish. [Use only one type of fish for your experiment, and control other variables such as light, food and temperature.]

6. What type of graph would be appropriate for this data set? Why?

A line graph is most appropriate because it can best display the relationship between the variables.

7. Graph the data from Table 4: Water Quality vs. Fish Population (found at the beginning of this exercise).

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8. Interpret the data from the graph made in Question 7.

The number of fish in the body of water increases along with dissolved oxygen up to about 12 ppm. When the concentration is higher than 12 ppm, the relationship is less clear. There may be an ideal dissolved oxygen concentration that supports the greatest number of fish, but that conclusion would require further testing.

Experiment 2: Experimental Variables (2 pts each part, 8 total/question)

Determine the variables tested in the each of the following experiments. If applicable, determine and identify any positive or negative controls.

1. A study is being done to test the affects of habitat space on the size of fish populations. Different sized aquariums are set up with six goldfish in each one. Over a period of six months, the fish are fed the same type and amount of food. The aquariums are equally maintained and cleaned throughout the experiment. The temperature of the water is kept constant. At the end of the experiment the number of surviving fish are surveyed.

A. Independent Variable: Habitat Space (Different sized aquariums are tested)

B. Dependent Variable: Size of Fish Populations (The number of surviving fish are surveyed)

C. Controlled Variables/Constants: Type of food, amount of food, equal maintenance and cleaning, water temperature

D. Experimental Controls/Control Groups: There are no control groups in this experiment.

2. To determine if the type of agar affects bacterial growth, a scientist cultures E. coli on four different types of agar. Five petri dishes are set up to collect results:

One with nutrient agar and E. coli

One with mannitol-salt agar and E. coli

One with MacConkey agar and E. coli

One with LB agar and E. coli

One with nutrient agar but NO E. coli

All of the petri dishes received the same volume of agar, and were the same shape and size. During the experiment, the temperature at which the petri dishes were stored, and at the air quality remained the same. After one week the amount of bacterial growth was measured.

A. Independent Variable: Type of agar (nutrient agar, mannitol-salt agar, MacConkey agar, LB agar)

B. Dependent Variable: Bacterial growth (after one week the amount of bacterial growth was measured)

C. Controlled Variables/Constants: Volume of agar, size and shape of petri dishes, temperature, air quality

D. Experimental Controls/Control Groups: One petri dish with nutrient agar, but no E. coli is a negative control because no growth should be seen if no E. coli was added

Exercise 3: Testable Observations (2 pts each)

Determine which of the following observations could lead to a testable hypothesis. For those that are testable:

Write a hypothesis and null hypothesis

What would be your experimental approach?

What are the dependent and independent variables?

What is your control?

How will you collect your data?

How will you present your data (charts, graphs, types)?

How will you analyze your data?

1. A plant grows three inches faster per day when placed on a window sill than it does when placed on a coffee table in the middle of a living room.

Hypothesis: Plants in the window sill grow faster due to increased light.

Null hypothesis: Increased light does not make plants grow faster.

Approach: Place two plants in the window. Leave one in the window and take the second plant

and let it spend different amounts of time in the light (decreased light exposure).

Dependent variable: Height of the plant. Independent variable: Amount of time spent in the sunlight by each plant.

Control: A plant remaining out of direct sunlight (but not in total darkness), like on the table.

Data collection: Measure the height of each plant every day for a week and record the total growth after one week.

Data presentation: Use a bar graph to show the results. Each of the three plants will have its own bar representing the height it grew in one week

Analyze: Look for an increase in growth with increased time on window sill.

2. The teller at the bank with brown hair and brown eyes and is taller than the other tellers.

No testable hypothesis - This is an observation, but it is a statement with no testable component.

3. When Sally eats healthy foods, her blood pressure is 10 points lower than when she eats fatty foods.

Hypothesis: A healthy diet leads to lower blood pressure.

Null hypothesis: A healthy diet doesn’t lead to lower blood pressure.

Approach: Collect blood pressure data over time for groups eating healthy foods and a group eating fatty foods.

Independent variable: Healthy or Unhealthy Diet

Dependent variable: Blood pressure (would be affected by the change in diet).

Controls: All groups should be exposed to similar amounts of exercise and stress.

Data collection: Test the blood pressure of your study subjects at fixed intervals over time - alwaysat the same time of day, under similar diet conditions.

Presentation: Use a line graph for individual evaluation over time. Use a bar graph to show the average blood pressure for each of your study groups.

Analyze: Look at data gathered over time to see whether diet lowered blood pressure.

4. The Italian restaurant across the street closes at 9 pm but the one two blocks away closes at 10 pm.

No testable hypothesis - This is a statement with no testable relationship.

5. For the past two days the clouds have come out at 3 pm and it has started raining at 3:15 pm.

For this particular, specific observation, you could not create a controlled experiment, so you could have said it's an observation only, and that would have been acceptable for the information given. If you did propose an experiment, since the the time appears to be the independent variable that the dependent variable (clouds) depends on, but that is not the case, you'd have to go further and propose what variables you're going to look at--what atmospheric conditions (that aren't observed in this case) are the variables related to the cloud formation? (So, you'd need additional observation before you could actually come up with a hypothesis. If you did make some assumptions about cloud formation and proposed a hypothesis, it might look something like this:

Hypothesis: As temperatures rise throughout the day, it increases the rate of evaporation, increasing the amount of moisture in the air. Temperatures and atmospheric water concentrations reach their maximum at mid-afternoon. Then, when temperatures begin to lower at about 3:00, clouds form and the evaporated moisture in the air condenses and it rains.

This experiment could be recreated in a microclimate, under lab conditions, or observed using daily weather station instruments to see if the pattern holds up.

Meteorologists can gather data about the atmospheric conditions to determine what variables are related to this and then develop experiments to see if their models work---looking for a correlation between those conditions and similar weather. Each observation would be a replication. Meteorologists gather a lot of data FIRST, then use it to make predictions--hypotheses--that they test by making more observations in the real world to compare with.

6. George did not sleep at all the night following the start of daylight savings.

Hypothesis: Daylight savings affected how much George was able to sleep.

Null hypothesis: Daylight savings did not affect how much George was able to sleep.

Approach: Study George’s sleeping habits before, during, and after daylight savings time.

Dependent variable: The number of hours George sleeps during daylight savings time.

Independent variable: The day/time.

Control: George’s average night’s sleep.

Data collection: Record George’s sleeping patterns for several weeks before, during, and after daylight savings time. Write down what time he goes to bed and how many hours he sleeps for each night.

Presentation: Use a line graph to plot the day/time on the x-axis and George’s hours of sleep on the y-axis.

Analyze: Use the data to show whether daylight savings time affected George’s sleep. Possible questions to answer with the data:

What did the graph look like leading up to the due date of George’s assignment? What happened around George’s paper’s due date? Did George’s sleeping patterns go back to normal after the assignment was due? If so, how long did it take?

Exercise 4: Unit Conversion

For each of the following, convert each value into the designated units.

1. 46,756,790 mg = 46.75679 kg

2. 5.6 hours = 20,160 seconds

3. 13.5 cm = 5.31 inches

4. 47 °C = 116 °F

Exercise 5: Accuracy vs. Precision

For the following, determine whether the information is accurate, precise, both or neither.

1. During gym class, four students decided to see if they could beat the norm of 45 sit-ups in a minute. The first student did 64 sit-ups, the second did 69, the third did 65, and the fourth did 67.

Precise because all the data is closely together, but not accurate since it is far from the norm of 45 sit ups.

2. The average score for the 5th grade math test is 89.5. The top 5th graders took the test and scored 89, 93, 91 and 87.

Both precise and accurate, because all the scores are closely gathered around the average score.

3. Yesterday the temperature was 89 °F, tomorrow it’s supposed to be 88 °F and the next day it’s supposed to be 90 °F, even though the average for September is only 75 °F degrees!

The data is precise, but not accurate.

4. Four friends decided to go out and play horseshoes. They took a picture of their results shown to the right:

Both accurate and precise.

5. A local grocery store was holding a contest to see who could most closely guess the number of pennies that they had inside a large jar. The first six people guessed the numbers 735, 209, 390, 300, 1005 and 689. The grocery clerk said the jar actually contains 568 pennies.

Neither precise or accurate.

Exercise 6: Significant Digits and Scientific Notation

Part 1: Determine the number of significant digits in each number and write out the specific significant digits.

1. 405000 = 3 significant digits – 4,0,5

2. 0.0098 = 2 significant digits – 9,8

3. 39.999999 = 8 significant digits – 3,9,9,9,9,9,9,9

4. 13.00 = 4 significant digits – 1,3,0,0

5. 80,000,089 = 8 significant digits – 8,0,0,0,0,0,8,9

6. 55,430.00 = 7 significant digits – 5,5,4,3,0,0,0

7. 0.000033 = 2 significant digits – 3,3

8. 620.03080 = 8 significant digits – 6,2,0,0,3,0,8,0

Part 2: Write the numbers below in scientific notation, incorporating what you know about significant digits.

1. 70,000,000,000 = 7 x 10^10

2. 0.000000048 = 4.8 x 10^-8

3. 67,890,000 = 678.9 x 10^5

4. 70,500 = 70.5 x 10^3

5. 450,900,800 = 450900.8 x 10^3

6. 0.009045 = 904.5 x 10^-5

7. 0.023 = 2.3 x 10^-2