To test the claim about the population mean $\mu$ using the sample statistics provided, we need to establish the null and alternative hypotheses.

Given Information:

• Claim: $\mu < 4715$
• Significance level: $\alpha = 0.01$
• Sample mean: $\overline{x} = 4817$
• Standard error: $SE = 5389$
• Sample size: $n = 55$

Hypotheses:

• The null hypothesis $H_0$ represents the assumption that the population mean is equal to or greater than the value specified by the claim.
• The alternative hypothesis $H_a$ represents the claim that the population mean is less than the specified value.

Null Hypothesis:

Since the claim is that the mean is less than 4715, the null hypothesis should be that the population mean is greater than or equal to 4715.

$H_0: \mu \geq 4715$

Alternative Hypothesis:

The alternative hypothesis is based on the claim, which suggests that the population mean is less than 4715.

$H_a: \mu < 4715$

Summary:

• Null Hypothesis ($H_0$): $\mu \geq 4715$
• Alternative Hypothesis ($H_a$): $\mu < 4715$

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Would you like help with the next steps in the hypothesis testing process, such as calculating the test statistic or determining the p-value? Let me know if you have any questions or need further explanation.

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Related Questions:

1. How do you calculate the test statistic for a hypothesis test for the population mean?
2. What is the formula for the standard error in hypothesis testing?
3. How do you interpret the p-value in a hypothesis test?
4. What steps are involved in performing a one-tailed hypothesis test?
5. How do you determine whether to reject or fail to reject the null hypothesis?

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Tip: Always make sure to understand the direction of the claim to correctly form your alternative hypothesis. In this case, since the claim suggests "less than," the alternative hypothesis must reflect this.