Question

A realtor is interested to compare the average cost of a 3 bedroom home in three different cities.   Prices from a sample of homes in each city are collected and shown in the dataset shown below (data is shown in thousands of dollars).

The realtor is interested to know if the prices of the average 3 bedroom home are statistically the same for the three cities.    Use a significance level of 5%.

The realtor has confirmed that the samples were randomly selected and independent, and the populations have normal distribution and the population variances are equal.  

(a) calculate the Test Statistic for this example (round your answer to 2 decimal places)

(b) calculate the P-value for this example (round your answer to 2 decimal places)

"Housing Prices in Atlanta"   Housing Prices in Seattle   Housing Prices in Miami
344 331 295
332 273 295
360 378 317
332 374 293
301 329    333
312 372 295
361 320 324
355 292   406
360 289 312
269 363 357
277 342 385
376 322 349
360 354 422
398 342 361
298 342 337
314   323 385
341 336 337
340 367 334
390 419 328
348 320 347

Answer 1

Given -

A realtor is interested to compare the average cost of a 3-bedroom home in three different cities with 5% level of significance.

Cost of a 3-bedroom home for below cities are available.

· Housing Prices in Atlanta

· Housing Prices in Seattle

· Housing Prices in Miami

Sample of size n = 20 selected from each city.

Samples were randomly selected and independent.

The populations have normal distribution and the population variances are equal.

Using given information, we can setup the hypothesis for given problem

Null Hypothesis

H0 = Average cost of a 3-bedroom home in three different cities is same. I.e.: µA = µS = µM

Alternative Hypothesis

H1 = Average cost of a 3-bedroom home in three different cities is not same. I.e.: µA ≠ µS ≠ µM

To test this hypothesis, we conduct One-way ANOVA since we are comparing more than 2 means

Below is the output of one-way ANOVA

SUMMARY
Groups	Count	Sum	Average	Variance
Housing Prices in Atlanta	20	6768	338.4	1207.305
Housing Prices in Seattle	20	6788	339.4	1176.253
Housing Prices in Miami	20	6812	340.6	1372.779
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	48.53333	2	24.26667	0.019381	0.980812	3.158843
Within Groups	71370.4	57	1252.112
Total	71418.93	59

a) From above results we can observe that test statistic value/ F value is = 0.019381

b) P-value for this example is = 0.980812