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One Sample Hypothesis Testing Paper
Introduction
In the present housing market, it is decisive that houses are assigned competitive estimates
based on their locations. Taking into consideration the factors affecting a house’s price, the
cost effectiveness is escalated by everyone involved in the buying process. The price
comparison between the houses located at the heart of cities and those at the outskirts is
established by the team hypothesis. The team first determines the intention or the purpose
of the research and then, using the five-step process, evaluates the results. The focus of our
paper is to make the decision by stating the hypotheses and the decision rule and by
calculating the expected frequencies and test statistics.
One Sample Hypothesis Testing Paper
Our paper’s mission is to analyze the factors affecting housing prices. The problem
statement is to explore the relationship between distance from the centre of the city and
the prices of homes within a specific radius. The research question attempted to be
answered by our team is: Will the data reveal a significant difference in price for houses
less than 15 miles from the center of the city (Group 1) and those houses equal to or
greater than 15 miles from the center of the city (Group 2)?
The mean of home prices in Group 1 is designated as µH1and that of Group 2 as µH2.
1. Null Hypothesis: No statistically eminent differences between the means of home
prices in Group 1 and Group 2.
H0: µH1 = µH2
2. Alternate Hypothesis: There exists a statistically eminent difference between the
means of home prices in Group 1 and Group 2.
H1: µH1 ≠ µH2
Five Step Process
The five steps in the hypothesis test include: 1) State the hypothesis, 2) State the decision
rule, 3) Calculate the expected frequencies, 4) Calculate the test statistic and 5) Make the
decision (Doane and Seward, 2007).
Hypothesis
The problem statement is to explore the relationship between distance from the center of
the city and the price of homes, or will the data reveal an indicative difference in price for
houses less than 15 miles from the center of the city (Group 1) and those houses equal to or
greater than 15 miles from the center of the city (Group 2)? In other words, are the homes
situated at the heart of the city more expensive than those located at the outskirts of the
city?
Decision Rule
To ensure that the results are compelling and the probability of achieving these results is
less than .05, the critical value of this test will be .05. The 2 samples used are independent.
Our sample standard deviation, using Megastat, for Group 1 is 48.1. The list of home prices
in Group 1 is 52 and therefore ‘n’ is 52. Similarly, the sample standard deviation for Group
2 is 43.9 and its ‘n’ is 53.
Expected Frequencies
The curve in Group 1 is positive to the right as its mean is greater than its median. The right
curve or the right skew in Group 1 is .396 (using Megastat). Group 2 also has a positive
curve to the right due to the same reason as that of Group 1 and represents the right skew
as .530.
Test Statistic
Group 1 has a mean price of 232.0 with a standard deviation of 48.1 and is composed of
homes that are located less than 15 miles from the city. Group 2 has a mean price of 210.4
with a standard deviation of 43.9 and is composed of homes located equal to or more than
15 miles from the city. On the basis of a sample population of 105 and a confidence interval
of 95%, if the estimated t-value is greater than 1.984 and is found to the right of the critical
value in the normal distribution bell curve, then the null hypothesis will be rejected. If the
estimated t-value is less than 1.984 and falls to the left of the critical value on the normal
distribution bell curve, the null hypothesis will not be rejected (Doane and Seward, 2007).
Group 1: Less than 15 miles from city
Group 2:
Equal to or
more than 15 miles from city
The Decision
Based on the obtained data and the statistical calculations, it is evident that the mean price
of homes located within or less than 15 miles from the city is higher than those located on
the outskirts of the city. These results prove that we will be unsuccessful in rejecting the
null hypothesis (homes near the city are more expensive) and will abort the alternate
hypothesis (homes outside the city are more expensive.
The Results
Acceptance and rejection of the Ho hypothesis is based solely on the decision rule. The
critical value which builds the threshold for accepting or rejecting the hypothesis is
constituted by the experiment’s decision rule. The 2 samples used are independent. Group
1 has a mean price of 232.0 with a standard deviation of 48.1 and is composed of homes
that are located less than 15 miles from the city. Group 2 has a mean price of 210.4 with a
standard deviation of 43.9 and is composed of homes located equal to or more than 15
miles from the city. On the basis of a sample population of 105 and a confidence interval of
95%, if the estimated t-value is greater than 1.984 and is found to the right of the critical
value in the normal distribution bell curve, then the null hypothesis will be rejected. If the
estimated t-value is less than 1.984 and falls to the left of the critical value on the normal
distribution bell curve, the null hypothesis will not be rejected (Doane and Seward, 2007).
To ensure that the results are compelling and the probability of achieving these results is
less than .05, the critical value of this test will be .05.
Based on the average price of homes in Groups 1 and 2, the t-value is estimated to be 2.41.
This value is greater than 1.984 with a confidence interval of 95%. Hence, the null
hypothesis is rejected. After the completion of the hypothesis test using the decision rule
(reject H0 if the calculated t-value is greater than 1.984) and the design experiment, it was
concluded that the null hypothesis, which states that “there is no statistically significant
difference in the mean of home prices in group 1 and the mean of home prices in group 2”,
is rejected based on a confidence interval of 95%.
Conclusion
The most important factor that people consider while buying houses, is their location. The
research conducted by the team has proved the significance of location as one of the key
drivers of escalating prices of houses. The 95% confidence interval recognized by the team
proves the existence of a statistically significant difference between the means of home
prices in Group 1 and Group 2. Therefore, it has become crucial for realtors and homebuilders, in the present unstable economy, to uncover the gap in the pricings of houses
within the city and those outside the city.
References
Doane, D. and Seward, L. (2007). Applied statistics in Business and Economics.
McGraw-Hill. University of Phoenix RES 342 Text.