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Scenario

You have been hired by the Regional Real Estate Company to help them analyze real estate data. One of the company’s Pacific region salespeople just returned to the office with a newly designed advertisement. The average cost per square foot of home sales based on this advertisement is $280. The salesperson claims that the average cost per square foot in the Pacific region is less than $280. In other words, he claims that the newly designed advertisement would result in higher average cost per square foot in the Pacific Region. He wants you to make sure he can make that statement before approving the use of the advertisement. In order to test his claim, you will generate a random sample size of 750 using data for the Pacific region and use this data to perform a hypothesis test. 

Prompt

Generate a sample of size 750 using data for the Pacific region. Then, design a hypothesis test and interpret the results using significance level a = .05. You will work with this sample in the assignment. Briefly describe how you generated your random sample.

  • Hypothesis Test Setup: Define your population parameter, including hypothesis statements, and specify the appropriate test.
    • Define your population parameter.
    • Write the null and alternative hypotheses. Note: Remember, the salesperson believes that his sales are higher.
    • Specify the name of the test you will use.
      • Identify whether it is a left-tailed, right-tailed, or two-tailed test.
    • Identify your significance level.
  • Data Analysis Preparations: Describe sample summary statistics, provide a histogram and summary, check assumptions, and find the test statistic and significance level.
    • Provide the descriptive statistics (sample size, mean, median, and standard deviation).
    • Provide a histogram of your sample.
    • Describe your sample by writing a sentence describing the shape, center, and spread of your sample.
    • Determine whether the conditions to perform your identified test have been met.
  • Calculations: Calculate the p value, describe the p value and test statistic in regard to the normal curve graph, discuss how the p value relates to the significance level, and compare the p value to the significance level to reject or fail to reject the null hypothesis.
    • Calculate the sample mean and standard error.
    • Determine the appropriate test statistic, then calculate the test statistic.
      Note: This calculation is (mean – target)/standard error. In this case, the mean is your regional mean (Pacific), and the target is 280.
    • Calculate the p value.
      Note: For right-tailed, use the T.DIST.RT function in Excel, left-tailed is the T.DIST function, and two-tailed is the T.DIST.2T function. The degree of freedom is calculated by subtracting 1 from your sample size.
      Choose your test from the following:
      =T.DIST.RT([test statistic], [degree of freedom])
      =T.DIST([test statistic], [degree of freedom], 1)
      =T.DIST.2T([test statistic], [degree of freedom])
    • Using the normal curve graph as a reference, describe where the p value and test statistic would be placed.
  • Test Decision: Discuss the relationship between the p value and the significance level, including a comparison between the two, and decide to reject or fail to reject the null hypothesis.
    • Discuss how the p value relates to the significance level.
    • Compare the p value and significance level, and make a decision to reject or fail to reject the null hypothesis.
  • Conclusion: Discuss how your test relates to the hypothesis and discuss the statistical significance.
    • Explain in one paragraph how your test decision relates to your hypothesis and whether your conclusions are statistically significant.

Summary Statistics for MAT 240 Real Estate Data (for dataset in Modules 2, 3, and 4)

n Mean Median Std. Dev. Min Q1 Q3 Max

Listing

price ($)

1,000 342,365 318,000 125,914 135,300 265,250 381,600 987,600

Cost per

square

foot ($)

1,000 169 166 41 71 139 191 344

Square

feet

1,000 2,111 1,881 921 1,101 1,626 2,215 6,516

This graph shows the frequency for listing price.

This graph shows the frequency for square feet.

New England

House Listing Price Data by Region
Regional sample (n = 1001)
State County Region House listing price Cost per square foot Square footage
CT litchfield New England $327,050 $173 1,888
ME penobscot New England $167,500 $106 1,586
NH merrimack New England $297,950 $138 2,152
VT washington New England $287,950 $147 1,959
ME york New England $389,550 $227 1,719
VT washington New England $220,500 $132 1,670
NH strafford New England $309,471 $164 1,885
MA suffolk New England $707,050 $562 1,259
MA norfolk New England $722,050 $327 2,210
NH hillsborough New England $665,500 $318 2,090
RI washington New England $362,950 $194 1,871
NH belknap New England $522,050 $279 1,869
VT rutland New England $312,950 $157 1,993
RI newport New England $251,800 $118 2,128
MA franklin New England $602,050 $334 1,800
ME penobscot New England $253,050 $158 1,600
VT washington New England $180,050 $95 1,896
MA berkshire New England $323,050 $159 2,032
ME kennebec New England $402,950 $238 1,695
NH cheshire New England $210,050 $106 1,981
VT franklin New England $289,550 $165 1,750
CT new london New England $242,950 $131 1,848
NH merrimack New England $313,000 $144 2,174
NH merrimack New England $337,950 $155 2,176
NH hillsborough New England $322,950 $159 2,036
CT windham New England $381,950 $237 1,615
VT washington New England $227,000 $120 1,888
CT new london New England $318,050 $193 1,648
CT new haven New England $291,500 $169 1,724
MA plymouth New England $302,950 $149 2,028
MA franklin New England $221,800 $125 1,780
NH cheshire New England $258,500 $141 1,838
CT new haven New England $277,050 $155 1,790
ME penobscot New England $157,750 $99 1,588
NH grafton New England $257,300 $140 1,840
VT washington New England $297,050 $161 1,850
ME york New England $337,050 $190 1,772
CT new haven New England $270,421 $153 1,763
MA suffolk New England $762,050 $568 1,341
NH grafton New England $251,850 $145 1,741
RI newport New England $596,050 $275 2,170
MA middlesex New England $653,000 $272 2,400
MA franklin New England $297,050 $152 1,960
CT new london New England $272,950 $225 1,212
RI providence New England $277,050 $184 1,504
MA barnstable New England $597,950 $311 1,920
CT litchfield New England $396,050 $175 2,268
NH belknap New England $293,000 $159 1,838
NH belknap New England $267,950 $149 1,797
MA suffolk New England $797,050 $608 1,311
RI kent New England $273,050 $179 1,524
CT new haven New England $256,500 $182 1,410
VT windsor New England $347,050 $164 2,120
CT litchfield New England $327,950 $185 1,776
NH cheshire New England $232,550 $126 1,845
NH cheshire New England $256,864 $131 1,968
NH hillsborough New England $339,444 $160 2,126
RI washington New England $487,950 $269 1,812
CT middlesex New England $340,450 $182 1,874
CT new london New England $292,050 $155 1,880
NH strafford New England $282,950 $156 1,819
MA suffolk New England $772,500 $569 1,359
MA bristol New England $383,050 $205 1,873
MA bristol New England $373,050 $198 1,880
RI kent New England $317,950 $207 1,537
MA suffolk New England $720,500 $565 1,275
MA hampden New England $237,950 $143 1,668
ME kennebec New England $180,050 $107 1,678
MA suffolk New England $880,550 $636 1,385
VT chittenden New England $395,500 $183 2,162
CT hartford New England $261,707 $141 1,850
VT washington New England $277,050 $158 1,752
NH strafford New England $295,550 $160 1,852
CT hartford New England $245,750 $169 1,452
MA bristol New England $397,500 $215 1,847
CT new london New England $315,050 $167 1,884
MA norfolk New England $622,950 $270 2,303
RI bristol New England $497,950 $223 2,234
NH rockingham New England $408,050 $188 2,170
NH merrimack New England $277,950 $138 2,016
MA hampden New England $237,950 $143 1,664
NH merrimack New England $281,525 $141 2,002
VT rutland New England $197,950 $107 1,857
ME kennebec New England $232,050 $131 1,768
VT chittenden New England $357,050 $174 2,050
ME androscoggin New England $195,443 $116 1,679
MA hampden New England $222,994 $129 1,726
NH rockingham New England $407,950 $197 2,066
CT litchfield New England $355,050 $162 2,185
MA hampshire New England $303,050 $159 1,907
NH grafton New England $207,050 $120 1,732
CT new london New England $268,000 $160 1,680
CT fairfield New England $724,550 $274 2,645
VT washington New England $275,050 $142 1,936
NH rockingham New England $439,950 $210 2,099
MA plymouth New England $487,550 $238 2,050
ME penobscot New England $136,864 $86 1,596
MA norfolk New England $575,500 $260 2,214
MA plymouth New England $447,050 $224 2,000
VT chittenden New England $375,086 $179 2,100
RI kent New England $252,950 $163 1,555
VT franklin New England $227,050 $126 1,799
MA worcester New England $297,950 $158 1,881
NH cheshire New England $204,550 $108 1,893
RI washington New England $522,950 $288 1,817
NH rockingham New England $412,950 $189 2,182
MA hampden New England $238,000 $136 1,749
CT windham New England $193,950 $119 1,632
CT middlesex New England $317,300 $173 1,832
VT franklin New England $187,050 $106 1,766
MA berkshire New England $367,050 $183 2,010
MA hampshire New England $347,500 $176 1,974
CT tolland New England $243,000 $133 1,830
NH merrimack New England $285,550 $130 2,195
ME penobscot New England $136,550 $86 1,583
NH grafton New England $257,050 $140 1,840
RI washington New England $527,950 $281 1,880
ME kennebec New England $188,000 $105 1,798
CT middlesex New England $307,050 $155 1,978
MA berkshire New England $365,050 $181 2,016
NH hillsborough New England $311,739 $151 2,061
NH merrimack New England $290,500 $131 2,214
MA berkshire New England $357,750 $176 2,031
VT washington New England $293,050 $154 1,900
MA middlesex New England $623,950 $279 2,237
MA franklin New England $225,550 $119 1,890
MA franklin New England $227,950 $127 1,792
VT rutland New England $187,550 $102 1,843
VT chittenden New England $344,550 $168 2,050
RI providence New England $230,500 $155 1,483
VT chittenden New England $355,950 $172 2,072
MA worcester New England $312,950 $161 1,938
ME androscoggin New England $170,450 $101 1,681
VT rutland New England $183,050 $100 1,839
MA hampden New England $216,007 $129 1,678
VT chittenden New England $362,950 $173 2,104
ME york New England $360,500 $207 1,742
ME kennebec New England $167,950 $99 1,700
MA franklin New England $226,500 $128 1,775
MA essex New England $555,050 $265 2,097
CT litchfield New England $310,500 $222 1,396
VT franklin New England $223,050 $124 1,800
NH grafton New England $214,550 $126 1,705
ME york New England $327,500 $186 1,762
CT new london New England $270,500 $150 1,800
MA suffolk New England $770,980 $611 1,263
CT fairfield New England $740,550 $279 2,653
MA barnstable New England $563,050 $297 1,898
CT fairfield New England $732,500 $264 2,774
RI newport New England $570,500 $288 1,982
MA franklin New England $227,950 $120 1,902
CT middlesex New England $307,050 $154 1,988
NH merrimack New England $308,050 $140 2,208
ME cumberland New England $367,950 $200 1,841
NH merrimack New England $298,050 $138 2,158
MA hampden New England $207,800 $127 1,635
MA berkshire New England $357,050 $177 2,016
ME york New England $327,950 $189 1,734
MA middlesex New England $605,450 $288 2,103
CT hartford New England $214,800 $128 1,682
ME penobscot New England $127,950 $83 1,550
MA barnstable New England $554,049 $291 1,904
CT middlesex New England $312,950 $182 1,722
VT washington New England $232,550 $128 1,820
ME penobscot New England $122,950 $78 1,574
MA worcester New England $283,000 $153 1,845
VT rutland New England $207,050 $104 2,000
NH grafton New England $187,050 $112 1,674
RI newport New England $558,050 $275 2,026
MA middlesex New England $597,500 $286 2,089
ME cumberland New England $347,407 $191 1,823
MA hampshire New England $323,050 $182 1,778
RI washington New England $477,050 $262 1,824
VT rutland New England $178,050 $95 1,882
VT windsor New England $327,050 $152 2,148
CT middlesex New England $308,050 $170 1,808
CT litchfield New England $316,300 $189 1,674
VT washington New England $227,950 $127 1,800
ME penobscot New England $127,550 $81 1,582
NH hillsborough New England $353,050 $164 2,157
MA bristol New England $397,950 $207 1,922
MA suffolk New England $777,050 $613 1,267
VT rutland New England $217,193 $109 1,996
MA hampshire New England $302,500 $154 1,958
MA suffolk New England $737,050 $546 1,351
NH grafton New England $205,050 $117 1,752
MA middlesex New England $677,050 $300 2,260
NH strafford New England $257,500 $138 1,872
NH cheshire New England $227,050 $122 1,854
ME kennebec New England $169,000 $99 1,700
ME cumberland New England $325,050 $181 1,800
MA bristol New England $328,000 $174 1,888
RI kent New England $255,500 $168 1,518
NH belknap New England $282,950 $154 1,842
VT franklin New England $220,500 $125 1,769
CT new london New England $295,050 $155 1,900
VT franklin New England $193,050 $112 1,728
ME york New England $357,564 $206 1,732
NH hillsborough New England $326,950 $159 2,058
MA berkshire New England $364,550 $178 2,044
ME cumberland New England $327,500 $175 1,871
MA essex New England $497,950 $249 2,000
ME york New England $338,050 $192 1,765
RI providence New England $237,950 $155 1,534
VT windsor New England $313,050 $145 2,158
VT windsor New England $277,050 $139 1,992
MA hampden New England $215,550 $130 1,663
VT franklin New England $220,050 $122 1,800
VT chittenden New England $360,427 $175 2,062
VT chittenden New England $363,050 $177 2,046
NH strafford New England $266,550 $149 1,790
MA suffolk New England $767,050 $553 1,388
MA middlesex New England $622,500 $293 2,121
NH hillsborough New England $320,050 $147 2,171
VT washington New England $277,050 $147 1,881
VT washington New England $202,950 $122 1,668
CT tolland New England $250,579 $139 1,807
MA worcester New England $327,950 $165 1,985
CT new haven New England $257,950 $162 1,588
MA worcester New England $303,050 $160 1,899
MA berkshire New England $353,050 $174 2,025
ME kennebec New England $144,300 $89 1,631
MA bristol New England $348,000 $191 1,825
CT new haven New England $267,050 $150 1,778
MA barnstable New England $595,050 $301 1,977
CT windham New England $217,050 $138 1,568
MA barnstable New England $557,050 $292 1,909
VT chittenden New England $372,950 $173 2,151
CT tolland New England $274,800 $137 2,005
MA barnstable New England $548,911 $288 1,903
NH hillsborough New England $308,000 $147 2,098
RI newport New England $590,079 $292 2,022
MA bristol New England $363,050 $194 1,872
NH strafford New England $265,050 $141 1,876
ME cumberland New England $307,950 $171 1,800
MA barnstable New England $552,950 $303 1,822
MA bristol New England $337,050 $181 1,858
MA hampshire New England $317,950 $165 1,928
NH grafton New England $210,500 $120 1,752
MA hampden New England $175,050 $112 1,561
CT tolland New England $243,050 $133 1,821
MA middlesex New England $640,550 $294 2,180
NH belknap New England $308,000 $161 1,919
CT fairfield New England $688,479 $242 2,843
MA hampden New England $217,950 $134 1,622
MA middlesex New England $635,543 $297 2,141
NH hillsborough New England $348,721 $159 2,192
CT fairfield New England $717,050 $271 2,649
MA barnstable New England $553,050 $284 1,946
MA worcester New England $315,500 $168 1,881
MA hampden New England $207,950 $127 1,636
CT windham New England $229,050 $143 1,601
ME androscoggin New England $163,050 $97