The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7  auto accidents per day with a standard deviation of  0.06 The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.06 . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null H0 hypothesis  and the alternative hypothesis H1 that we would use for this test.
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In this problem, we are testing the actuaries' claim that the standard deviation of the number of accidents per day is no longer 0.06. The goal of the hypothesis test is to determine whether the standard deviation has changed from the previous value.

Here's how we can set up the hypotheses for this test:

- **Null Hypothesis (\(H_0\)):** The standard deviation of the number of accidents per day is still equal to 0.06.
  \[
  H_0: \sigma = 0.06
  \]

- **Alternative Hypothesis (\(H_1\)):** The standard deviation of the number of accidents per day is different from 0.06. This implies that the standard deviation has either increased or decreased.
  \[
  H_1: \sigma \neq 0.06
  \]

This is a two-tailed test because we are interested in any change (whether the standard deviation has increased or decreased) rather than a change in just one direction.

Would you like further details on how to perform this hypothesis test or any other questions?

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Here are 5 related questions that could help expand on this topic:
1. How do we compute the test statistic for testing the standard deviation?
2. What is the appropriate distribution for testing standard deviations (variance)?
3. How do we determine the critical values for a two-tailed test?
4. How does sample size affect the hypothesis test for the standard deviation?
5. What is the relationship between variance and standard deviation in hypothesis testing?

**Tip:** The Chi-Square distribution is typically used when testing hypotheses about variances and standard deviations.

The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.7 auto accidents per day with a standard deviation of 0.06. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.06. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null H0 hypothesis and the alternative hypothesis H1 that we would use for this test.

Learn how to perform a hypothesis test for the standard deviation of auto accidents. This example focuses on testing whether the standard deviation has changed from 0.06 using a two-tailed test with the Chi-Square distribution. Suitable for college-level statistics students.

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