Question: Suppose we want to know whether or not the mean weight of a certain species of turtle is equal to 310 pounds. To test this, we will perform a one-sample t-test at significance level $\alpha = 0.05$. a. State the Null Hypothesis and Identify the claim: (2pts) H₀: ________________________________________________ H₁: ________________________________________________ b. Set the Level of Significance: (1pt) $\alpha$: __________________ c. Calculate the t-critical Value ($t_{critical}$) (2pts) $t_{critical}$: __________________ d. Compute the one sample t-test Value: (5pts) e. Decision Rule (draw the bell curve): (10pts) f. State the Conclusion: (5pts)

1. **Problem Statement:** We want to test if the mean weight $\mu$ of a species of turtle is equal to 310 pounds using a one-sample t-test at significance level $\alpha = 0.05$. 2. **Hypotheses:** - Null hypothesis $H_0$: $\mu = 310$ (the mean weight is 310 pounds). - Alternative hypothesis $H_1$: $\mu \neq 310$ (the mean weight is not 310 pounds). 3. **Level of Significance:** - Given $\alpha = 0.05$. 4. **Formula for t-test statistic:** $$t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$$ where: - $\bar{x}$ = sample mean - $\mu_0$ = hypothesized population mean (310 pounds) - $s$ = sample standard deviation - $n$ = sample size 5. **Calculate the critical t-value:** - For a two-tailed test at $\alpha = 0.05$, the critical values are $\pm t_{\alpha/2, df}$ where $df = n-1$. - Use a t-distribution table or calculator with degrees of freedom $df$. 6. **Compute the t-test value:** - Substitute the sample statistics into the formula. - Show intermediate steps including simplification and cancellation if any. 7. **Decision Rule:** - If $|t| > t_{critical}$, reject $H_0$. - Otherwise, fail to reject $H_0$. 8. **Conclusion:** - Based on the decision rule, state whether there is enough evidence to conclude the mean weight differs from 310 pounds or not. *Note:* Since the problem does not provide sample data ($\bar{x}$, $s$, $n$), the numerical calculation of $t$ and $t_{critical}$ cannot be completed here. **Summary:** - $H_0: \mu = 310$ - $H_1: \mu \neq 310$ - $\alpha = 0.05$ - $t = \frac{\bar{x} - 310}{s/\sqrt{n}}$ - Decision: reject $H_0$ if $|t| > t_{critical}$ This completes the setup and explanation for the one-sample t-test for the turtle mean weight problem.