An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.6 minutes. A random sample of 34 dive durations has a mean of 12.4 minutes and a standard deviation of 2.2 minutes. At $\alpha=0.10$ is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$. \[ \begin{array}{l} H_{0}: \mu=11.6 \\ H_{a}: \mu=11.6 \end{array} \] (Type integers or decimals, Do not round, The claim is the null hypothesis. (b) Use technology to find the P-value. Find the standardized test statistic, $t$. \[ t= \] (Round to two decimal places as needed.)

Step 1 ：Identify the claim and state the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis is that the mean dive duration is 11.6 minutes, and the alternative hypothesis is that the mean dive duration is not 11.6 minutes. So, we have \(H_{0}: \mu=11.6\) and \(H_{a}: \mu \neq 11.6\). The claim is the null hypothesis.

Step 2 ：Calculate the t-statistic using the formula: \(t = \frac{{\text{{sample mean}} - \text{{population mean}}}}{{\text{{sample standard deviation}} / \sqrt{{\text{{sample size}}}}}}\). Given a sample mean of 12.4 minutes, a population mean of 11.6 minutes, a sample standard deviation of 2.2 minutes, and a sample size of 34, the calculated t-statistic is approximately 2.12.

Step 3 ：Calculate the p-value. The p-value is a probability that provides a measure of the evidence against the null hypothesis provided by the data. The smaller the p-value, the stronger the evidence against the null hypothesis. The calculated p-value is approximately 0.042.

Step 4 ：Compare the p-value with the significance level (0.10). If the p-value is less than the significance level, we reject the null hypothesis. Since the p-value (0.042) is less than the significance level (0.10), we reject the null hypothesis.

Step 5 ：Conclude that there is enough evidence to reject the oceanographer's claim that the mean dive duration of a North Atlantic right whale is 11.6 minutes. The final answer is: The t-statistic is approximately \(\boxed{2.12}\) and the p-value is approximately \(\boxed{0.042}\).