Question

A real estate agent claims the median sales price of homes in Happy Valley is over $198,000.

Test the agents claim based on the following random sample of homes:

$228,000   $191,450   $147,500   $202,600   $133,800   $219,000   $207,000   $218,000

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 198000
Alternative Hypothesis, Ha: μ > 198000

Rejection Region
This is right tailed test, for α = 0.05 and df = 7
Critical value of t is 1.895.
Hence reject H0 if t > 1.895

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (193418.75 - 198000)/(34620.4929/sqrt(8))
t = -0.374

P-value Approach
P-value = 0.6403
As P-value >= 0.05, fail to reject null hypothesis.

No, the prices are not more than 198000