Hypothesis Testing:

As a result of an intense review of our statistical analysis, many conclusions were brought forward as a result of our testing. Beginning with confidence intervals we discovered many interesting characteristics of Kalamazoo College students as well as Kalamazoo citizens.With a 95% confidence interval we can conclude that Kalamazoo citizens consider movies their favorite entertainment activity.They also spend between $-9.82754 and $162.17842 on their favorite entertainment activity. These people have average household incomes between $52,209.0656 and $69,054.0924. Kalamazoo College students, on the other hand, spend between $5.0276 and $13.5500 on their favorite entertainment activity.Kalamazoo College students come from households with average incomes between $103,809.07289 and $132,397.82371.

Additional data was derived from mathematical hypothesis testing, in which we consistently used a 95% confidence interval. Hypothesis testing was very useful when comparing our data to nationally found trends and statistics that we gathered from reputable sources, such as the US Census Bureau. The first of our findings was in response to data that we received from the Bureau of Labor Statistics^. Although the U.S. Department of Labor: Bureau of Labor Statistics³ concluded that non-college graduates make up 60.5% of the total expenditures on entertainment spending, this is not the case with our sample as only 4.1935% of expenditures are those of non-college graduates.

Another interesting discovery is that out of our sample, those who are less than 35 years of age only spent $3390 of the $107,429 total documented expenditures, or 3.156%.This caused our null hypothesis of 22%, derived from a study conducted by the U.S. Department of Labor: Bureau of Labor Statistics. This could be due to the higher than average household income of the average Kalamazoo College student.

Further analysis led us to discover that only 1.8235% of average total expenditures of Kalamazoo College students went towards fees and admissions. This data shows a dramatic variation from studies that suggest that this number should be around 25.685%.

The final informative statistic that we received from our hypothesis testing was based on a study about Midwestern spending₄, which suggests that 23.6063% of entertainment expenditures went towards fees and admissions for the 25 years of age and under age group. Our sample of Kalamazoo College students, all of whom are under 25 years of age, spend 17.2989% of their expenditures on fees and admissions.

Further testing of hypothesis in terms of proportions further led us to conclusions about our sample. The first test we ran was comparing the different entertainment expenditures of the men and women of Kalamazoo College.  Our findings reviled that women's entertainment spending exceeds those of fellow male students, even thought our confidence interval suggests that men exceed women in entertainment spending.

Another hypothesis test that we completed compared the spending of Kalamazoo College students with non-students, that is, Kalamazoo citizens. Our results revealed, to our surprise, that Kalamazoo citizens spend more on entertainment items than Kalamazoo College students.

Regression Testing:

One final type of testing, regression, disclosed the relationship between many of our variables. The first regression test that we completed was between the amount of total spending (our Y variable) and age, number of people over the age of 18 in the household, hours of work per week, and income (our explanatory or X variables). These tests revealed a significant and positive relationship between total entertainment spending and age, as well as total entertainment spending on number of people over 18 in the household. A third finding of this test expressed a similar relationship between total entertainment spending and hours of work per week.

Our next regression test looked at the relationship between the spending on fees and admissions (our Y variable) and gender, education, income, and whether the person is a Kalamazoo College student or Kalamazoo resident (our X variables). This test showed only one statistically significant relationship, that being the positive relationship between spending on fees and admissions and whether the person is a Kalamazoo College student or Kalamazoo resident.

Our final regression test examined the relationship between household income (our Y variable) and whether the person is a Kalamazoo College student or Kalamazoo resident, education, number of people over 18, and hours of work per week. From this analysis we found two statistically significant relationship. The first finding is a negative relationship between income and whether the person is a Kalamazoo College student or Kalamazoo resident. This is confirmed by our sample data where Kalamazoo College students' households' incomes' are roughly twice the average income of our Kalamazoo citizen sample group. The second finding was the positive relationship between income and education.