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State the null and alternative hypotheses you would use to test the following situation.

The American Automobile Association (AAA) claims that 54% of fatal car/truck accidents are caused by driver error. A researcher believes the percentage has decreased during the past year and tests the claim at the 10% level of significance.

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Final answer:

The null hypothesis (H0) for testing AAA's claim would be that the proportion of fatal accidents caused by driver error is 54% (H0: p = 0.54), while the alternative hypothesis (Ha) would denote a decrease in this proportion (Ha: p < 0.54). The test would be conducted at a 10% significance level.

Step-by-step explanation:

Defining Null and Alternative Hypotheses

To determine if the percentage of fatal car/truck accidents caused by driver error has decreased from the previously reported 54%, we need to establish the appropriate null and alternative hypotheses. The null hypothesis (H0) is the claim stating no change from the standard or previously known value, that is, we assume the proportion of driver error accidents remains the same (p = 0.54). The alternative hypothesis (Ha) represents the researcher's belief in the change, which in this case is that the proportion has decreased (p < 0.54).

Therefore, the two hypotheses for this test would be stated as:

  • H0: p = 0.54
  • Ha: p < 0.54

When performing the test at a 10% level of significance (alpha = 0.10), if the p-value calculated from the test statistic is less than alpha, the null hypothesis would be rejected, supporting the researcher's claim that the percentage has decreased.

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