Question

You are doing some research on the cost of one-bedroom apartments in town. Based on prices from previous years, a real estate agent gives you the information that σ is approximately $55 and μ is approximately$675per month. Assume that price follows roughly a normal distribution. You have randomly selected 25 apartments for which the price was published. You set the null and alternative hypotheses as follows:

?0: ?≤ 675 ?? ??: ?>675

a. With α=0.05, find the value of ?̅ that will lead to reject ?0.

b. If the true population mean is assumed to be 705, compute the power.

c. Graphically show α,β and power above.

Answer 1

(a) µ = 675

σ = 55

n = 25

z = -1.96

z = (x - µ)/σ/√n

-1.96 = (x - 675)/55/√25

x = 653.44

(b) The formula used is:

z = 1.96

σ = 55

n = 25

µ0 = 675

µ = 705

Plugging in all values, we get Power = 0.8608

(c) The graph is: