Question

1. Suppose you are asked to select a sample of Hampshire County 2016 single family home prices in order to estimate the 2017 mean price of homes in Hampshire County. Your firm uses the mean price when doing market analysis for the homes they list. The standard deviation for 2016 home prices was $50,000. Your firm wants a margin of error no larger than $15,000. Assuming the 2017 standard deviation will be equal to the 2016 standard deviation:

a. What size sample should you draw if you want a 95% level of confidence?

2. Because the population mean and standard deviation are unknown, you will need to use t‐values to create the confidence intervals. What are the appropriate t‐values for a:

a. 95% confidence interval?

Answer 1

1)

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 15000, σ = 50000

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 50000/15000)^2
n = 42.68

Therefore, the sample size needed to satisfy the condition n >= 42.68 and it must be an integer number, we conclude that the minimum required sample size is n = 43
Ans : Sample size, n = 43

2)

for α = 0.05 and df = 42
Critical value of t are -2.018 and 2.018.