Question

In: Statistics and Probability

An educational researcher interested in the consistency of school absenteeism over time studied a sample of...

  1. An educational researcher interested in the consistency of school absenteeism over time studied a sample of 8 high school students for whom complete high school records were available. The researcher counted the number of days of school each student missed while in the sixth grade and how many they missed while in the tenth grade. He obtained the following results:

                        Student # Days Missed in 6th Grade                        # Days Missed in 10th Grade          

                        A                                        4                                                                  10

                        B                                        2                                                                   4

                        C                                       21                                                                  11

                        D                                        1                                                                   3

                        E                                        3                                                                   1

                        F                                        5                                                                   5

                        G                                        4                                                                   9

                        H                                        8                        5                                         

  1. What is the strength and the direction of the association between the number of days missed in sixth grade and the number of days missed in tenth grade. Be sure to provide the statistic on which your answer is based.
  2. Can the correlation be generalized to the larger population of students? (You will need to perform a hypothesis test.) Explain your answer and show all necessary work.xplain your answer. You should write out the research and null hypotheses in Greek notation.

Solutions

Expert Solution

a)

The association between the number of days missed in sixth grade and the number of days missed in tenth grade is determined by Pearson correlation coefficient.

The Pearson correlation coefficient is obtained using the formula,

Where the data values are,

# Days Missed in 6th Grade, X # Days Missed in 10th Grade, Y
4 10 16 100 40
2 4 4 16 8
21 11 441 121 231
1 3 1 9 3
3 1 9 1 3
5 5 25 25 25
4 9 16 81 36
8 5 64 25 40
Sum 48 48 576 378 386

Now,

The Pearson correlation coefficient value, r = 0.6087 which indicates there is a positive correlation between two variable and the correlation value of r between 0.6 to 0.8 mean there is a strong correlation between two variable.

b)

Now, the hypothesis test for significance of the correlation coefficient is performed in following steps,

Step 1: The null and alternative hypotheses are,

Step 2: The significance level,

The critical value for the t-statistic for degree of freedom = n-2=8-2=6

(In excel use formula, =T.INV.2T(0.05,6) )

Step 3: The t-statistic is obtained using the formula,

Step 4:

Since the t-statistic is less than t-critical value, the null hypothesis is not rejected. Hence there is no significant correlation is between number of days missed in sixth grade and the number of days missed in tenth grade.


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