Two years old, the study showed that the mean price of all one-bedroom condos is 560 thousand dollars in a city.

Since the mortgage rate is very low during the COVID-19 pandemic, economists believed that the mean price of one-bedroom condos will be continuously increasing.

To support the claim, a random sample of one-bedroom condos is selected from the city during the COVID-19 pandemic, and their prices (in thousands of dollars) are shown below.

510

535

538

546

563

575

581

606

608

608

622

629

645

671

674

692

Part A - Suppose we want to test whether the claim is true or not.

1. [2] State the null and alternative hypotheses (symbolically).

1. [3] Calculate the test statistic and p-value for the hypothesis test. Assume the population standard deviation of the house prices is 50 thousand dollars.

1. [2] At the 5% significance level, what can you conclude?

Part B - Suppose we want to estimate the mean prices of all one-bedroom condos in the city during the COVID-19 pandemic.

1. [2] Calculate a 90% confidence interval for the parameter described above.

1. [1] Interpret the confidence interval you calculated in part(a).