A certain drug can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid refiux. The manufacturer of the drug claims that more than $92 \%$ of patients taking the drug are healed within 8 weeks. In clinical trials, 209 of 226 patients suffering from acid reflux disease were healed after 8 weeks. Test the manufacturer's claim at the $\alpha=0.1$ level of significance.

Because $n p_{0}\left(1-P_{0}\right)=\square \quad \mathbf{V} 10$, the sample size is $\square 5 \%$ of the population size, and the sample the requirements for testing the hypothesis $\overline{\mathbf{v}}$ satisfied.
(Round to one decimal place as needed.)

Step 1 ：Given data: sample size \(n = 226\), number of successes in the sample \(x = 209\), and hypothesized population proportion \(p_0 = 0.92\).

Step 2 ：Calculate the sample proportion \(p = \frac{x}{n} = \frac{209}{226} = 0.9247787610619469\).

Step 3 ：Calculate the test statistic \(Z = \frac{p - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} = \frac{0.9247787610619469 - 0.92}{\sqrt{\frac{0.92(1 - 0.92)}{226}}} = 0.26480771189405977\).

Step 4 ：The test statistic is approximately 0.26, which is less than the critical value of 1.28. Therefore, we do not reject the null hypothesis. This means that the data does not provide strong evidence to support the manufacturer's claim that more than 92% of patients taking the drug are healed within 8 weeks.

Step 5 ：Final Answer: \(\boxed{0.26}\)