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To solve this hypothesis test problem, we'll go through these steps:

### Part (a) - State the null and alternative hypotheses:

Let \( \mu_1 \) represent the mean appreciation rate for houses in Sun Beach and \( \mu_2 \) represent the mean appreciation rate for houses in North Arden.

- **Null Hypothesis (\( H_0 \))**: \( \mu_1 \leq \mu_2 \) (The mean appreciation rate in Sun Beach is less than or equal to that in North Arden).
- **Alternative Hypothesis (\( H_1 \))**: \( \mu_1 > \mu_2 \) (The mean appreciation rate in Sun Beach is greater than that in North Arden).

This is a one-tailed test because the hypothesis tests whether the mean appreciation rate in Sun Beach is **greater** than that in North Arden.

Next steps involve calculating the sample statistics (means and standard deviations) for both groups, then using a t-test for independent samples to determine if we can reject \( H_0 \) at the 0.10 level of significance.

Would you like me to continue with these calculations?

Can we conclude, at the 0.10 level of significance, that the mean appreciation rate of houses in Sun Beach is higher than the mean appreciation rate of houses in North Arden?

Learn how to perform a hypothesis test to compare the mean appreciation rates of houses in Sun Beach and North Arden at a 0.10 significance level. This example uses a one-tailed t-test to determine if Sun Beach's appreciation rates are significantly higher.

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