In a previous year, $55 \%$ of females aged 15 and older lived alone. A sociologist tests whether this percentage is different today by conducting a random sample of 450 females aged 15 and older and finds that 242 are living alone. Is there sufficient evidence at the $\alpha=0.01$ level of significance to conclude the proportion has changed?

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

Step 1 ：Define the null hypothesis as the proportion of females aged 15 and older living alone is still 55%, and the alternative hypothesis as the proportion has changed.

Step 2 ：Calculate the sample proportion (p_hat) as the number of females living alone divided by the total sample size, which is \( \frac{242}{450} = 0.538 \).

Step 3 ：Define the hypothesized proportion (p_0) as 0.55 and the sample size (n) as 450.

Step 4 ：Calculate the test statistic (z) using the formula \( z = \frac{p_{hat} - p_{0}}{\sqrt{\frac{p_{0} \cdot (1 - p_{0})}{n}}} \), which gives \( z = -0.52 \).

Step 5 ：Calculate the p-value based on the test statistic and the standard normal distribution, which gives a p-value of 0.60.

Step 6 ：Since the p-value is greater than the significance level of 0.01, we do not reject the null hypothesis.

Step 7 ：Therefore, there is not sufficient evidence at the 0.01 level of significance to conclude the proportion has changed.

Step 8 ：Final Answer: \(\boxed{No}\)