Introduction
The purpose of this statistical analysis is to test the claim that the average cost per square foot of
home sales in the Pacific region is less than $280. The test will help determine the effectiveness
of the newly designed advertisement to its rollout in the region. MS Excel RANDOM sampling
function was used to sort the population from smallest to largest. A decision was made to sample
the first 750 houses from the full dataset of Pacific region.
Hypothesis Test Setup
The population parameter in this analysis is the average (µ) cost per square foot of home
sales in the Pacific region.
The following are the null and alternative hypothesis for the test:
oNull Hypothesis (H0): The average cost per square foot of home sales in the
pacific region is equal to $280. (µ = 280).
oAlternative Hypothesis: The Average cost per square foot of home sales in the
Pacific region is greater than $280. (µ > 280).
The test that will be used in this analysis is one-sample t-test. It is appropriate for this test
because it examines whether the population mean is statistically different from a known
or hypothesized value. In this test the mean is known ($280) and the population standard
deviation is not known.
The right-tailed test will be used because it is testing if the mean cost per square foot of
home sales is greater than a $280.
Data Analysis Preparation
The descriptive statistics is summarized in the table below:
Descriptive Statistics
Mean $264
Median $200
Standard Deviation 161.04
Sample Size 750
The histogram is given below:
Summary of Sample: The histogram shows a right-skewed distribution with the center
around its mean ($264), which is higher than its median ($200). The standard deviation of
$161.04 indicates a large spread in the data, suggesting high variability in house prices
per square foot of home sales in the Pacific region for the sample of 750 houses.
The following test Assumptions have been met:
oThe sample is generated using a random sampling technique in the MS Excel.
oThe sample data is normally distributed, which is ideal considering the Central
Limit Theorem ( = 750).𝑛
oThe sample meet the assumption that each house price is independent of others.
The test significance level is α = 0.05. This significance level implies that there is a 5%
chance of rejecting the null hypothesis.
Calculations
Sample Mean and Standard Error:
oSample mean: 264
oSample Error: 5.88
Test statistic: -2.73
Conducting a right-tailed test using MS excel formula, p-value is 0.997
Considering that p-value (0.997) is large, the test statistic is close to zero and would be
positioned close to the center (mean) of the normal distribution graph.
Considering that the p-value of 0.997 represents the area of the test statistics and lies to
the right of the test statistics, it is positioned close to the center of the normal distribution
graph.
Test Decision
The relationship between p-value and significance level (α = 0.05) is given below:
oIf the p-value is less than α (0.05), reject the null hypothesis (H0).
oIf the p-value is greater than or equal to α (0.05), reject the null hypothesis (H0).
The decision: Considering that the p-value (0.997) is greater than the significance level (α
= 0.05), we fail to reject the null hypothesis.
Conclusion
The conclusion is that there is not enough statistical evidence to support the claim that the
average cost per square foot in the Pacific region equals $280. The findings are statistically
significant since the calculated p-value (0.997) is greater than the significance level (α = 0.05).
The result indicates that the newly designed advertisement would not lead to a significantly
higher average cost per square foot of home sale at the hypothesized mean of $280.
