Last year, the mean price of a single-family home in Vero Beach was found to be $156,492. This year, a real-estate researcher would like to determine if the mean single-family home price in Vero Beach is greater than $156,492.

a. [tex]H_0: \mu = 156,492[/tex], [tex]H_1: \mu < 156,492[/tex]

b. [tex]H_0: \mu \neq 156,492[/tex], [tex]H_1: \mu = 156,492[/tex]

c. [tex]H_0: \mu = 156,492[/tex], [tex]H_1: \mu > 156,492[/tex]

d. [tex]H_0: \mu = 156,492[/tex], [tex]H_1: \mu \neq 156,492[/tex]

In order to determine if the mean single-family home price in Vero Beach is greater than $156,492, we can perform a hypothesis test. We will use a one-sample t-test to compare the sample mean to the population mean. The null hypothesis would be that the mean single-family home price in Vero Beach is equal to $156,492, and the alternative hypothesis would be that it is greater than $156,492.

We would collect a sample of single-family home prices in Vero Beach and calculate the sample mean. We would then calculate the test statistic using the formula:

t = (sample mean - population mean) / (standard deviation / sqrt(sample size))

If the calculated t-value is greater than the critical t-value at the desired significance level, we would reject the null hypothesis and conclude that the mean single-family home price in Vero Beach is indeed greater than $156,492.

Learn more about Hypothesis Testing here:

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