A simple random sample of 10 pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results $n=10, \bar{x}=65.8$ words, $s=15.7$ words. Given that this dictionary has 1441 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.6 words. Use a 0.10 significance level to test the claim that the mean number of words per page is greater than 48.6 words. What does the result suggest about the claim that there are more than 70,000 defined words? Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. Assume that the nnnulation is normally dictrihuted Determine the test statistic. (Round to two decimal places as needed.)

Step 1 ：Given that a simple random sample of 10 pages from a dictionary is obtained. The numbers of words defined on those pages are found, with the results $n=10$, $\bar{x}=65.8$ words, $s=15.7$ words. The dictionary has 1441 pages with defined words. The claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.6 words. We are to use a 0.10 significance level to test the claim that the mean number of words per page is greater than 48.6 words.

Step 2 ：We identify the null and alternative hypotheses. The null hypothesis is that the mean number of words per page is equal to 48.6 words. The alternative hypothesis is that the mean number of words per page is greater than 48.6 words.

Step 3 ：We calculate the test statistic using the formula: $t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step 4 ：Substituting the given values into the formula, we have $\bar{x} = 65.8$, $\mu_0 = 48.6$, $s = 15.7$, and $n = 10$.

Step 5 ：The test statistic is calculated to be approximately 3.46.

Step 6 ：Final Answer: The test statistic is \(\boxed{3.46}\).