The problem shown in the image seems to deal with a hypothesis test for the mean of a population. Here's a summary of the relevant parts:

Problem Details:

• Claim: The weights of quarters made after 1964 have a mean of 5.670 grams, as per mint specifications.
• Sample:
  • Size: $n = 33$
  • The test statistic is given as $t = -2.313$
• Significance level: $\alpha = 0.10$

Tasks:

1. State the null and alternative hypotheses:

   • Null hypothesis ($H_0$): $\mu = 5.670$ grams (The mean weight is 5.670 grams).
   • Alternative hypothesis ($H_1$): $\mu \neq 5.670$ grams (The mean weight is different from 5.670 grams).

2. Test statistic: The test statistic $t$ is provided as $-2.313$, which is the calculated value for this test.

Conclusion:

You are asked to interpret the result based on the $p$-value and the significance level of $0.10$. Generally, if the $p$-value is less than $\alpha$, you reject the null hypothesis.

Now you can calculate the $p$-value using the test statistic or refer to the $t$-distribution table. Let me know if you'd like help with the next steps, including calculating or interpreting the result!

Do you have any further questions about this problem? Here are 5 questions to expand the understanding:

1. What are the degrees of freedom for this $t$-test?
2. How do you interpret the $p$-value in hypothesis testing?
3. What is the critical value for $t$ at a 0.10 significance level with $n-1$ degrees of freedom?
4. How is the $t$-statistic calculated?
5. Can the null hypothesis be rejected or not, based on the test statistic?

Tip: Always ensure to check whether the test is one-tailed or two-tailed, as this affects the interpretation of the $p$-value and critical values.