Age and Size of Cash Offer – A consumer organization studied the effect of age on the size of cash

1. Age and Size of Cash Offer – A consumer organization studied the effect of age on the size of cash offer given to a person selling a used car.  The study involved a total of 36 people, 12 in each of three age groups (young, middle, and elderly) who acted as the owner of a used car. The same medium price, 6-yr-old car was taken to 36 different dealers and a cash offer was solicited for the car. Randomization was used in assigning the owner to the dealer.  The amount of the cash offer was recorded in $100s, so the first observation in the table below was an offer of $2300. Note that one of the elderly subjects decided not to participate at the last minute, so the sample sizes were 12, 12, and 11 respectively. SPSS was used to provide some descriptive statistics.

a.

a.  An ANOVA was conducted to test that the null hypotheses of equality of the population mean amount of cash for the three age populations, namely, H₀:  μ₁= μ₂ = μ₃  at the 5% level.  The ANOVA table below provides the sum of squares for between-groups, the sum of squares for error (within-groups), and the sum of squares for total. The sum of squares between the groups is given by ≈ 310.2.  Show the details for how this sum of squares was found (just substitute the values into all three terms that were summed to obtain this ≈ 310.2 value). (1

pts)

b.

B. Is the following statement true or false? The formula for the calculation of the MSE = 2.562 is an extension of the formula we used for the pooled variance estimate when conducting the two independent samples pooled t-test, namely s_p² = [(n₁ – 1)s₁² + (n₂ – 1)s₂²] / (n₁ + n₂ – 2).

            i. True

ii. False

c. To conduct an ANOVA, we must assume that the model for the response (amount of cash offer) for each of the three populations is normal with possibly different population means but equal population standard deviations. Which of the following is the best estimate of that common population standard deviation?

i. 155.097

ii. 2.562

iii. 3.3962

iv. 1.6006

d. Report the test statistic value and corresponding p-value.

e. Which of the following is the distribution that SPSS used to calculate the p-value?

i. N(0,1) distribution

ii. t distribution with 32 degrees of freedom

iii. F distribution with 2 and 32 degrees of freedom

f. At this point in the analysis, which of the following is the appropriate conclusion (using a 0.05 level of significance)?

i. There does not appear to be any difference between the population mean cash offers between the three age populations.

ii. It appears that at least one population mean cash offer is different for the three age populations.