Question

A certain company will purchase the house of any employee who is transferred out of state and will handle all details of reselling the house. The purchase price is based on two assessments, one assessor being chosen by the employee and one by the company. Based on the sample of eight assessments shown, do the two assessors agree? Use the .05 level of significance.

Assessments of Eight Homes ($ thousands)
Assessed by	Home 1	Home 2	Home 3	Home 4	Home 5	Home 6	Home 7	Home 8
Company	329	347	458	277	291	283	532	743
Employee	315	344	479	287	304	284	520	765

(a) Choose the appropriate hypotheses. Assume d = company assessed value – employee assessed value.

H₀: μ_d = 0 versus H₁: μ_d ≠ 0.

H₀: μ_d ≠ 0 versus H₁: μ_d = 0.

(b) State the decision rule for .05 level of significance. (Round your answers to 2 decimal places. A negative value should be indicated by a minus sign.)

Reject the null hypothesis if t_calc <  or t_calc >  .

(c-1) Find the test statistic t_calc. (Round your answer to 2 decimal places. A negative value should be indicated by a minus sign.)

t_calc             

(c-2) What is your conclusion?

We  (Click to select)  reject  fail to reject   the null hypothesis.

Answer 1

Difference Scores Calculations

Treatment 1

N₁: 8
df₁ = N - 1 = 8 - 1 = 7
M₁: 407.5
SS₁: 186536
s²₁ = SS₁/(N - 1) = 186536/(8-1) = 26648


Treatment 2

N₂: 8
df₂ = N - 1 = 8 - 1 = 7
M₂: 412.25
SS₂: 198467.5
s²₂ = SS₂/(N - 1) = 198467.5/(8-1) = 28352.5


T-value Calculation

s²_p = ((df₁/(df₁ + df₂)) * s²₁) + ((df₂/(df₂ + df₂)) * s²₂) = ((7/14) * 26648) + ((7/14) * 28352.5) = 27500.25

s²_M1 = s²_p/N₁ = 27500.25/8 = 3437.53
s²_M2 = s²_p/N₂ = 27500.25/8 = 3437.53

t = (M₁ - M₂)/√(s²_M1 + s²_M2) = -4.75/√6875.06 = -0.06

The t-value is -0.05729. The p-value is .955126

Fail to reect null