Exploring Data

What does a scatterplot show?

• Relationship between a quantitative and a categorical variable

• Relationship between two categorical variables

• Relationship between two qualitative variables

• Relationship between two quantitative variables

Which variable measures the outcome of a study in a scatterplot?

• Response Variable

• Correlation Coefficient

• Lurking Variable

• Explanatory Variable

What does a correlation near zero correspond to?

• Weak association

• Moderate association

• Strong association

• No association

What is the ideal way to picture associations between two quantitative variables?

• Bar graphs

• Histograms

• Pie charts

• Scatterplots

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire as seen in the table. The table provides the two estimates for each tire (in thousands of miles) What is the response variable?

• Distance traveled

• Time

• Method for estimating wear

• Tire number

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire as seen in the table. The table provides the two estimates for each tire (in thousands of miles) Is the data paired or not paired? How do you know?

• Paired because there are not two observations for each tire

• Paired because there are two observations for each tire

• Unpaired because there are not two observations for each tire

• Unpaired because there are two observations for each tire

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire as seen in the table. The table provides the two estimates for each tire (in thousands of miles). If you calculated the mean difference and got 3.732, what would this mean in context of the problem? (Note, I am not saying that this is the mean difference)

• On average, tires were estimated to travel 3.732 thousands of miles more using the "weight" method.

• On average, tires were estimated to travel 3.732 thousands of miles more using the "groove" method.

• On average, tires were estimated to travel 3.732 thousands of miles less using the "weight" method.

Researchers were interested in comparing two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves of the tire. A random sample of 16 tires was obtained. Both methods were used to estimate the total distance traveled by each tire as seen in the table. The table provides the two estimates for each tire (in thousands of miles). Describe how to simulate the distribution of the mean difference (Weight - Groove) using notecards.

• For each tire, use two notecards. Label one card with the tire's estimated distance using the weight method and one card with the estimated distance using the groove method. Shuffle the two cards & assign 1 card to weight & 1 to groove. Calculate the simulated diff. Do this for all 16 tires, and calculate the simulated mean difference. Record this value on a dot plot & repeat from shuffle 99 times.

• For each tire, use two notecards. Label one card with the tire's estimated distance using the weight method and one card with the estimated distance using the groove method. Shuffle the two cards & assign 1 card to weight & 1 to groove. Calculate the simulated diff. Do this for all 16 tires, and calculate the simulated mean difference. Record this value on a dot plot & repeat from shuffle 100 times.

• For each tire, use two notecards. Label one card with the tire's estimated distance using the weight method and one card with the estimated distance using the groove method. Shuffle all the cards & assign 2 cards to each tire. Calculate the mean diff. Record this value on a dot plot & repeat from shuffle 99 times.

Does exercises improve reaction time? Francie & Sebastian used an online game to measure the reaction of 15 randomly selected students from their school before and after each student had run two laps on a track.

Select the dot plot that correctly displays the difference in reaction time (Before - After) for each student.

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Does exercises improve reaction time? Francie & Sebastian used an online game to measure the reaction of 15 randomly selected students from their school before and after each student had run two laps on a track. Describe how to simulate the distribution of mean difference (Before - After) using notecards.

• For each student, use 2 notecards. Label 1 card with the student's before time and 1 card with the student's after time. Shuffle the 2 cards & assign 1 card to before & 1 card to after. Calc the simulated diff (Before - After). Do this for all 15 students & calculate the simulated mean diff. Record this value on a dotplot & repeat from shuffle 99 times.

• For each student, use 2 notecards. Label 1 card with the student's before time and 1 card with the student's after time. Shuffle all the cards and assign two cards to each students. Find the mean difference. Record this value on a dot plot & repeat from shuffle 99 times.