Question

Marty	206424
Rose	346150
Carter	372360
Peterson	310622
Carter	496100
Peterson	294086
Carter	228810
Isaacs	384420
Peterson	416120
Isaacs	487494
Rose	448800
Peterson	388960
Marty	335610
Rose	276000
Rose	346421
Isaacs	453913
Carter	376146
Peterson	694430
Rose	251269
Rose	547596
Marty	214910
Rose	188799
Carter	459950
Isaacs	264160
Carter	393557
Isaacs	478675
Carter	384020
Marty	313200
Isaacs	274482
Marty	167962
Isaacs	175823
Isaacs	226498
Carter	316827
Carter	189984
Marty	366350
Isaacs	416160
Isaacs	308000
Rose	294357
Carter	337144
Peterson	299730
Rose	445740
Rose	410592
Peterson	667732
Rose	523584
Marty	336000
Marty	202598
Marty	326695
Rose	321320
Isaacs	246820
Isaacs	546084
Isaacs	793084
Isaacs	174528
Peterson	392554
Peterson	263160
Rose	237120
Carter	225750
Isaacs	848420
Carter	371956
Carter	404538
Rose	250090
Peterson	369978
Peterson	209292
Isaacs	190032
Isaacs	216720
Marty	323417
Isaacs	316210
Peterson	226054
Marty	183920
Rose	248400
Isaacs	466560
Rose	667212
Peterson	362710
Rose	265440
Rose	706596
Marty	293700
Marty	199448
Carter	369533
Marty	230121
Marty	169000
Peterson	190291
Rose	393584
Marty	363792
Carter	360960
Carter	310877
Peterson	919480
Carter	392904
Carter	200928
Carter	537900
Rose	258120
Carter	558342
Marty	302720
Isaacs	240115
Carter	793656
Peterson	218862
Peterson	383081
Marty	351520
Peterson	841491
Marty	336300
Isaacs	312863
Carter	275033
Peterson	229990
Isaacs	195257
Marty	194238
Peterson	348528
Peterson	241920

Adam Marty recently joined North Valley Real Estate and was assigned twenty homes to market and show. When he was hired, North Valley assured him that the twenty homes would be fairly assigned to him. When he reviewed the selling prices of his assigned homes, he thought that the prices were much below the average of $357,000. Adam was able to find the data of how the other agents in the firm were assigned to the homes. Use statistical inference to analyze the “fairness” that homes were assigned to the agents

Answer 1

First we segregate the data between Adam and the other agents.

The average price of homes assigned to Marty is $ 270,896.3

The average price of homes assigned to other agents is $ 377,292.4

On the surface the assumption made by Adam is true, however, we can perform a statistical analysis to validate the claim.

We will set the hypothesis that:

H0: The homes were assigned fairly to all the agents.

H1: Adam was unfairly assigned homes that were below the average of $357,000.

Under the null hypothesis we can calculate the test statistic as:

+_ [(x1 - x2) SE

where = 24450.99

SE = sqrt(s/nl) + s/n 2)

with 72 degrees of freedom using the formula

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

The value of the t statistic is 4.3514 and the corresponding p value is 0.0000219

Since the p-value is much less than 0.05 we reject the null hypothesis at 5% level of significance and conclude that Adam Marty has been unfairly assigned homes with selling price much less than the average of $357000.