Question

ages of homes whiting, indiana leads the \top 100 cities with the oldest houses\ list with the average age of houses being 66.4 years. farther down the list resides franklin, pennsylvania, with an average house age of 59.4 years. researchers selected a random sample of 22 houses from whiting and 19 houses from franklin and obtained the following statistics. at \\( \alpha = 0.05 \\), can it be concluded that the houses in whiting are older? use the \\( p \\)-value method. assume the variables are normally distributed and the variances are unequal.

(a) state the hypotheses and identify the claim.

Explanation:

Step1: Identify the claim

The problem asks if houses in Whiting are older, so the claim is that \( \mu_1 > \mu_2 \) (where \( \mu_1 \) is Whiting's mean age, \( \mu_2 \) is Franklin's).

Step2: Formulate null hypothesis

The null hypothesis is the statement of no difference, so \( H_0: \mu_1 = \mu_2 \).

Step3: Formulate alternative hypothesis

Since the claim is that Whiting's houses are older, the alternative hypothesis is \( H_1: \mu_1 > \mu_2 \), which represents the claim.

Answer:

Null hypothesis: \( H_0: \mu_1 = \mu_2 \) (The average age of houses in Whiting is equal to that in Franklin)
Alternative hypothesis: \( H_1: \mu_1 > \mu_2 \) (The average age of houses in Whiting is older than that in Franklin)
Claim: The houses in Whiting are older (corresponds to \( H_1 \))