Explore BrainMass

Explore BrainMass

    Hypothesis test : T test in Megastat

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Implement raw data tables and computations, using both graphical and tabular methods of displaying data and results

    The US economy is in crisis brought on by the financial markets, the deep slump of the housing, high unemployment, and the slowdown of consumer spending. This has caused problems for buyers and sellers in the real estate industry. Even in this downturn, there are still people looking for homes and this is a buyers' market. Because of the slow US economy, there is an abundance of homes available for purchase brought on by high unemployment, and foreclosures.
    Because of the abundance of homes on the market, buyers are able to purchase more amenities, such as homes with more than one bedroom, bathrooms, a pool, and with more square footage. Even in this stalled economy, those additional amenities all have an impact on the selling price of a home. The objective of this research using the Real Estate Data sets will determine if there is a difference in the mean price per square foot between three and four bedroom homes. The sample will consist of 26 three bedroom and 26 four bedroom homes. This research will determine if the hypotheses should be accepted or rejected. Given the data mentioned above:
    The verbal hypothesis the research will determine if there is a difference in the mean price per square foot between three and four bedroom homes.. The mean for the three bedroom homes is 2,165 with a standard deviation of 210. The mean for the four bedroom homes is 2,308 with a standard deviation of 251. The hypothesis will determine if the price square foot is equal or not equal between the two samples.
    The numerical hypothesis is:
    H0: µ1 = µ2
    H1: µ1 ≠ µ2

    Five-Step Hypothesis Test

    As stated, the information given gives us
    3 Bedrooms 4 Bedrooms
    x1 = 2165 x2 = 2308
    s1 = 210 s2 = 251
    n1 = 26 n2 = 26

    The hypothesis tests are:
    H0: µ1 = µ2
    H1: µ1 ≠ µ2

    Therefore, the following represents data used and steps taken to verify the hypothesis using the five step process.
    Descriptive statistics 4 bedroom

    Size
    count 26
    mean 2,307.69
    sample variance 63,138.46
    sample standard deviation 251.27
    minimum 1900
    maximum 2900
    range 1000

    population variance 60,710.06
    population standard deviation 246.39

    standard error of the mean 49.28

    confidence interval 95.% lower 2,206.20
    confidence interval 95.% upper 2,409.18
    half-width 101.49

    empirical rule
    mean - 1s 2,056.42
    mean + 1s 2,558.97
    percent in interval (68.26%) 73.1%
    mean - 2s 1,805.14
    mean + 2s 2,810.24
    percent in interval (95.44%) 92.3%
    mean - 3s 1,553.87
    mean + 3s 3,061.51
    percent in interval (99.73%) 100.0%

    Descriptive statistics 3 bedroom

    Size
    count 26
    mean 2,165.38
    sample variance 43,953.85
    sample standard deviation 209.65
    minimum 1600
    maximum 2500
    range 900

    population variance 42,263.31
    population standard deviation 205.58

    standard error of the mean 41.12

    confidence interval 95.% lower 2,080.70
    confidence interval 95.% upper 2,250.06
    half-width 84.68

    empirical rule
    mean - 1s 1,955.73
    mean + 1s 2,375.04
    percent in interval (68.26%) 65.4%
    mean - 2s 1,746.08
    mean + 2s 2,584.69
    percent in interval (95.44%) 96.2%
    mean - 3s 1,536.43
    mean + 3s 2,794.34
    percent in interval (99.73%) 100.0%

    Calculations
    Degrees of freedom = v = 50 n1 + n2 - 2
    Two-tail critical value = t = (+-) 2.009 Appedix D table in text
    Significance value = a = 0.05 95% Confidnece Level

    Pooled varience sp2 is (n1 - 1)s12+(n2 - 1)s22 53550.5 2677525
    sp2 = 53550.50 n1 + n2 - 2 50

    Using sp2 the test statistic is x1-x2
    (assuming equal variance) t = -2.2281 SQRT(sp2/n1 +sp2/n2) -2.228055212

    Pooled standard deviation is sp
    sp = 231.4098 SQRT(sp2) 231.4098096
    (sp lies between s1 and s2 therefore the arithmetic is correct.)

    The test statistic t = -2.2281 falls within the rejection region so we can reject the hypothesis of equal means.

    P-value p = 0.0304 0.030401527

    Using sp2 the test statistic is x1-x2
    (assuming unequal variance) t = -2.2281 SQRT(s12/n1 +s22/n2) -143
    64.18153341 44100 63001

    Welch-Satterthwaite test [(s12/n1)+(s22/n2)]2 16968379 4119.269231
    Degrees of freedom = v' = 48 ((s12/n1)2/n1-1)+((s22/n2)2/n2-1) 349937.0415 1696.153846 2876937.87 115077.5148
    Two-tail critical value = t = (+-) 2.011 2423.115385 5871488.167 234859.5267

    Assumption Test Statistic d.f. Critical Value Decision
    Case 1 (equal variances) t = -2.2281 50 t = (+-) 2.009 Reject
    Case 2 (unequal variances) t = -2.2281 48 t = (+-) 2.011 Reject

    Implement raw data tables and computations, using both graphical and tabular methods of displaying data and results

    © BrainMass Inc. brainmass.com June 3, 2020, 10:19 pm ad1c9bdddf
    https://brainmass.com/statistics/students-t-test/hypothesis-test-t-test-in-megastat-226326

    Attachments

    Solution Summary

    The solution provides step by step method for the calculation of ANOVA for real estate data set . Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

    $2.19

    ADVERTISEMENT