Question

Assignment 6: Testing Correlations

Directions

Use the Bivatiate Correlation function and the Options submenu to answer each of the questions based on the scenario.

Scenario

The superintendent has continued the examination of data by examining the relationship between attendance rate and percent of students eligible for free or reduced priced lunch. The district data used for the analysis are contained below.

School	% Free or Reduced	Attendance Rate
1	47.2	94.8
2	31.1	96.1
3	58.9	94.9
4	44.9	94.2
5	24.1	95.7
6	52.4	94.8
7	54.7	93.8
8	68.1	92.6
9	49.6	93.6
10	42.9	93.8
11	38.1	92.8
12	27.2	95.7
13	58.4	93.4
14	52.4	93.6
15	58.4	94.6
16	64.9	93.0
17	75.5	92.9
18	35.6	95.1
19	79.4	92.8
20	67.3	92.6
21	54.7	95.5
22	74.7	91.8

Questions

1. What is the mean percent of students receiving free or reduced lunch? What is the mean attendance rate?
2. What are the standard deviations for the percent of students receiving free or reduced lunch and attendance rate?
3. State an appropriate null hypothesis for this analysis.
4. What is the value of the correlation coefficient?
5. Based on the value of the correlation coefficient, how would you classify the strength of this relationship?
6. Based on the information from the scenario, what is the appropriate value for the degrees of freedom?
7. What is the reported level of significance?
8. Present the results as they might appear in an article. This must include a table and narrative statement that reports and interprets the results of your analysis.

Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

Answer 1

A) Mean can be calculated as follows:

Mean = Sum of all values/Number of values

The mean percent of students receiving free or reduced lunch = 52.75

The mean attendance rate = 94.0045

b) The standard deviation can be calculated using the following command (=stdev.s)

C) Null and Alternate Hypothesis

Null Hypothesis: Ho - There is no significant relationship between attendance rate and % free or reduced lunch

Alternate Hypothesis: Ha - There is a significant relationship between attendance rate and % free or reduced lunch

D) Correlation Coefficient

Following formula can be used to calculate the correlation coefficient:

The correlation can be calculated as follows:

Since the value of correlation coefficient is nearly approaching zero, there is weak relationship between the two variables

Degree of freedom = (n1 + n2 -2) = (22+22-2) = 42

The level of significance can be assumed as 0.05.

Therefore, it can be concluded that, there is no significant relationship between the two variables.