Question 1

Think about driving in the United States. What data would you collect to answer the question “Which state has  the worst drivers?”

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Question 2

Suppose the nationwide proportion of fatal accidents that involve alcohol is 0.30.

1. What type of value, a parameter or a statistic, is the proportion of fatal accidents that were alcohol related?
2. Based on guidance from your instructor, select your own sample of size 10 [latex](n = 10)[/latex] from the nationwide population of fatal accidents. Record the proportion of fatal accidents that were alcohol related in your sample.
3.  Plot the proportion from Part B on the class dotplot, and make sure to sketch the final class dotplot in your notebook.
4. Describe the center, shape, and spread of the dotplot. Label the true  population proportion.

Question 3

In 2012, 38% of all fatal accidents in Texas were alcohol related, which is tied for 5th highest among the 50 states and DC.^[1] Suppose researchers wanted to analyze the  impact of a new alcohol awareness program on the number of alcohol-related fatal  accidents, so they recorded whether or not alcohol was involved in a random sample of 50 fatal accidents in Texas.

1. Are the data recorded on whether or not alcohol was involved from a sample of fatal accidents in Texas or from the population of all fatal accidents in  Texas?
2.  In this scenario, what type of value, a parameter or a statistic, is the proportion of fatal accidents that were alcohol related?
3. What type of value is the proportion of all Texas drivers who have been  involved in fatal collisions and were alcohol-impaired?

Question 4

Let’s sample from all fatal accidents using technology. Suppose that the proportion  of all fatal accidents in Texas has not changed since 2012.

1. What is the value of the population proportion?
2. Go to the DCMP Sampling Distribution of the Sample Proportion tool at https://dcmathpathways.shinyapps.io/SampDist_prop/ and draw one sample of sample size [latex]n = 50[/latex] using these inputs:
   • Select the box titled “Enter Numerical Values for n and p.”
   • Enter the value for [latex]p[/latex] from Part a and [latex]n = 50[/latex].
   • Select how many samples (of size 50) you want to simulate drawing from the population.
   • Select “Draw Sample(s).”
   • Note: The sample proportion, [latex]p[/latex], will be displayed in the graph labeled “Data Distribution (Bar Graph from last generated sample).”

   What is the sample proportion, [latex]\hat{p}[/latex], that you got for your sample?

3. If you draw another sample of sample size [latex]n = 50[/latex]., do you think the sample proportion, [latex]\hat{p}[/latex], will change? Explain.

Question 5

Now draw 100 samples of sample size [latex]n = 50[/latex].

1. If you were to create a dotplot for the generated samples, similar to Question 2, Part c, how many “dots” would be on the plot?
2. What is the last sample proportion, [latex]\hat{p}[/latex], for [latex]n = 50[/latex] that was drawn?
3. The graph at the bottom of the tool represents the approximate sampling distribution. What is the mean of the approximate sampling distribution for the sample proportion?
4. Compare the mean from the sampling distribution to the proportion from the population distribution.

Question 6

Suppose the researchers found that 18 of the 50 fatal accidents sampled were alcohol related.

1. What is the sample proportion collected by the researchers? Use proper notation.
2. Suppose the news reported the following headline after seeing the results of the study:

   “The alcohol awareness program has successfully decreased the alcohol-related accidents from 38% to 36%. Thus, we should increase the funding substantially to continue to fund this successful program.”

   Should the news have been so confident in their reporting? Explain.