Assignment 3

One-sample t-test

The expenditure variable chosen was the Annual Household Income variable named as “SE-Income.” A one-sample t-test was used to investigate whether annual household income data has a mean equal to $9,500 (hypothesized mean). The test was conducted using SPSS, s statistical software used mainly for social studies. Before conducting the test, the following assumptions were made.

Assumptions

First, it is assumed that the variable data is continuous, that is, measure at interval or ratio level. The second assumption is that the data is are not correlated or have any relations (independent). Thirdly, the data should be approximately normally distributed. However, in some cases, this assumption may be violated and still produce accurate results. Lastly, the data must not have significant outliers. Outliers are data entries and are different from the rest of the dataset. Presence of an outlier may jeopardize the normality of the dataset and cause wrong result and misleading interpretation.

Test data Result

The result of the One-sample test at a 95 percent confidence interval is presented in table 1 below.

Table SEQ Table * ARABIC 1: One-sample t-test result for annual household income

One-Sample Test

Test Value = 95000

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower

Upper

Annual Household Income

4.504

29

.000

4535.967

2476.05

6595.89

From the output data, the mean annual household income (99535.97±5516.57) was higher than the hypothesized mean of 95,000. Since the p-value =0.01 is less than the significance value of 0.05, it can be concluded that the mean annual household is statistically significantly different from the population mean of 95000, t29=4.504, p=0.01.

Moreover, the mean difference in the population means is 4535.97, and the 95% confidence intervals (95% CI) of the difference are 2476.05 to 6595.89. Therefore, we can conclude that annual household income was statistically significantly higher by 4535.97 (95% CI, 2476.05 to 6595.89) than a normal annual household income of $95,000, t(29)= 4.504, p = 0.01.

Two Sample Hypothesis Test Analysis

In this test, the amount of annual expenditure in dollars between married and unmarried individuals was compared.

Research Question

Is there a difference between the annual expenditure of married people and the annual expenditure of the unmarried people?

Hypothesis

Null Hypothesis, H0:μ1=μ2 (there is no statistically significant difference between the annual expenditure of married people and that of unmarried people).

Alternative Hypothesis, H1:μ1≠μ2 (there is a statistically significant difference between the annual expenditure of married people and that of unmarried people).

The result was analyzed using SPSS software and data presented in Table 2 below.

Table SEQ Table * ARABIC 2: Independent sample t-test result testing whether there is a difference between the annual expenditure of married and unmarried people.

Independent Samples Test

Levene’s Test for Equality of V