Can someone review my work? I need help distinguishing the meaning of my calculations ...

The purpose of this report will determine whether the region of New England's housing prices and square footage are significantly different from the national market. My approach is to calculate a series of tests that will help me make the decision to reject or fail to reject the null hypothesis. The tests that I will be utilizing for my research are one-tailed and two-tailed testing strategies. To generate my random sample for the New England region, in Excel, I used the formula =RAND, which lead me to use the first 100 data samples generated. The states that are going to be included in my sample are: Massachusetts, Vermont, Rhode Island, Connecticut, New Hampshire, and Maine. My null hypothesis is regional mean listing price = national mean listing price ($288,407). My alternate hypothesis is that the regional mean will be greater than the national mean.

After selecting my sample set of data from New England, I have determined two hypothesis questions and which test would be most appropriate for each. For my first hypothesis question, I will be analyzing if the housing prices in New England are equal to those on the national market. I will be using a right-tailed test to look at the population parameter of the 100 homes within my New England Region. The test statistic is $24.89. Next, I will be analyzing if the square footage in the home of New England different than those of the homes in the national market. The test-statistic being 3.19. The test that I am going to use for this is a two-tailed test.

1-Tail Test

My population parameter is the housing price mean of $358,599.

Write null and alternative hypotheses. Note: For means, define a hypothesis that is greater than the population parameter. Specify your significance level.]

Data analysis: [Summarize your sample data using appropriate graphical displays and summary statistics.]

Mean

Standard Deviation

Median

Housing Price

$358,599

157920.4

299.059

Square Footage

1,851

259.4358

1,854

This dataset is from my random sample in the New England region of 100 homes. The histogram above appears to be ___ with outliers ____ in the _____ range. Also, notice at the highest point, which is also the mode, the data set is in the ___ range.

Test Statistic: $22.48

T =(358599-2990500)(157920.4/sqrt(100))

P-value =5.6E-41

P = t.dist.rt(22.48,100)

To sum up all this information, the p-value is less than 0.05, which means that there is a statistical significance, and I must reject the null hypothesis. This actively demonstrates that the housing prices in New England are significantly higher than the national average.

2-Tail Test

The population parameter for this set of data for the square footage is 1,851. Null hypothesis: Regional mean square footage is equal to the national mean square footage of 1,944. My alternative hypothesis is the regional mean square footage will not equal the national mean square footage of 1,944.

Level of significance: XXXX

Mean

Standard Deviation

Median

Housing Price

$358,599

157920.4

299.059

Square Footage

1,851

259.4358

1,854

The shape of the histogram appears to be _______________. There are or aren't any outliers? What is the highest point of the dataset?

T = 1.984217

P-value = 1.12E-40

For this dataset we reject the null hypothesis due to the p-value being less than 0.05. The p-value for the square footage is 1.12E-40, which means .....

Comparison of the Test Results:

[Calculate the 95% confidence interval and show or describe the method of calculation.]

[Interpret the confidence 95% confidence interval in context.]

Final Conclusions

[Summarize Your Findings: Refer back to Step 1 and summarize your findings of the sample you selected.]

[Discuss: Discuss if you were surprised by the findings including why or why not.]

_______________________________________________________________________________________________

Template:

Introduction

Purpose: [Include in this section a brief overview, the purpose of the report, and your approach. Define your random sample and two hypotheses (means) to analyze.]

Sample: [Take a random sample of observations from your region and describe what is included in your sample (i.e., states, region, years or months).]

Questions and type of test: [For your selected sample, define two hypothesis questions and the appropriate type of test hypothesis for each. For each hypothesis question, answer questions 3a-c from the Project Two Guidelines and Rubric. This includes questions about the population parameter, your hypothesis, the inference method you will use, and how you will use estimation and confidence intervals to help you solve the problem.]

1-Tail Test

Hypothesis: [Define the population parameter. Write null and alternative hypotheses. Note: For means, define a hypothesis that is greater than the population parameter. Specify your significance level.]

Data analysis: [Summarize your sample data using appropriate graphical displays and summary statistics.]

[Provide at least one histogram of your sample data.]

[In a table, provide summary statistics including sample size, mean, median, and standard deviation.]

Note: For quartiles 1 and 3, use the quartile function in Excel:

=QUARTILE([data range], [quartile number])

[Summarize your sample data, describing the center, spread, and shape in context.]

[Note: For shape, think about the distribution: skewed or symmetric.]

[Check the assumptions by determining if the normal condition has been met. Determine if there are any other conditions that you should check and whether they have been met.]

[Note: Think about the central limit theorem and sampling methods.]

Hypothesis Test Calculations:

[Determine the appropriate test statistic (t).]

[Note: This calculation is (mean - target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.]

[Calculate the probability (p value).]

[Note: This calculation is done with the T.DIST.RT function in Excel: =T.DIST.RT([test statistic], [degree of freedom]). The degree of freedom is calculated by subtracting 1 from your sample size.]

Interpretation:

[Relate the p value and significance level.]

[Make the correct decision (reject or fail to reject).]

[Provide a conclusion in the context of your hypothesis.]

2-Tail Test

Hypotheses: [Define the population parameter. Write null and alternative hypotheses.]

[Note: For means, define a hypothesis that is not equal to the population parameter.]

[State your significance level.]

Data Analysis:

[Summarize your sample data using appropriate graphical displays and summary statistics.]

[Provide at least one histogram of your sample data.]

[In a table, provide summary statistics including sample size, mean, and standard deviation.]

[Note: For quartiles 1 and 3, use the quartile function in Excel:

=QUARTILE([data range], [quartile number]) ]

[Summarize your sample data, describing the center, spread, and shape in comparison to the national information.]

[Note: For shape, think about the distribution: skewed or symmetric.]

[Check the assumptions by determining if the normal condition has been met. Determine if there are any other conditions that you should check and whether they have been met.]

Note: Think about the central limit theorem and sampling methods.

Hypothesis Test Calculations:

[Determine the appropriate test statistic (t).]

[Note: This calculation is (mean - target)/standard error. In this case, the mean is your regional mean, and the target is the national mean.]

[Calculate the probability (p value).]

[Note: This calculation is done with the TDIST.2T function in Excel: =T.DIST.RT([test statistic], [degree of freedom]). The degree of freedom is calculated by subtracting 1 from your sample size.]

Interpretation:

[Relate the p value and significance level.]

[Make the correct decision (reject or fail to reject).]

[Provide a conclusion in context to your hypothesis.]

Comparison of the Test Results:

[Calculate the 95% confidence interval and show or describe the method of calculation.]

[Interpret the confidence 95% confidence interval in context.]

Final Conclusions

[Summarize Your Findings: Refer back to Step 1 and summarize your findings of the sample you selected.]

[Discuss: Discuss if you were surprised by the findings including why or why not.]

Data analysis: [Summarize your sample data using appropriate graphical displays and summary statistics.] House Listing Prices 45 40 35 30 25 20 15 10 5 O ($277,050, $397,050] ($517,050, $637,050] ($757,050, $877,050] [$157,050, $277,050] ($397,050, $517,050] ($637,050, $757,050] ($877,050, $997,050] Mean Standard Deviation Median Housing Price $358.599 157920.4 299.059 Square Footage 1,851 259.4358 1,854square footage of 1,944. Level of significance: XXXX Square footage 35 30 25 20 15 10 5 [ 1,212 , 1,412 ] ( 1,412, 1,612 ] (1,612, 1,812 ] (1,812 , 2,012 ] ( 2,012 , 2,212 ] ( 2,212 , 2,412 ] ( 2,412 , 2,612 ] ( 2,612 , 2,812 ] Mean Standard Deviation Median Housing Price $358.599 157920.4 299.059 Square Footage 1,851 259.4358 1,854