Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE) (Aliaga et al. ,2005) project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level. What is the first contribution to the ² statistic for the significance test to test for a relationship between ease of learning SAS and SAS proficiency based on the location of cell A?

A) 6
B) 11
C) 7.2
D) None of the above

Question

Because statistical software plays such an important role in modern statistical applications,many studies have encouraged the use of technology in statistics courses.The Guidelines for the Assessment and Instruction in Statistics Education (GAISE) (Aliaga et al. ,2005) project was funded by the American Statistical Association to examine needs for college level statistics courses.One of the six recommendations from GAISE is the use of technology for developing conceptual understanding and analyzing data.A survey was sent to students at 100 different universities across the United States to access the relationship between ease of learning the statistical software program SAS and a student's currently level of SAS proficiency.The results of the survey are published in Jackson et al. ,2011,in the International Mathematical Forum journal and are shown below. Table 1.Two-way table for ease of learning SAS and SAS proficiency level.

What is the first contribution to the ² statistic for the significance test to test for a relationship between ease of learning SAS and SAS proficiency based on the location of cell A?

A) 6
B) 11
C) 7.2
D) None of the above

Yi?it Yalç?nta? · Accepted Answer

Final Answer : C, Explanation :  To find the contribution to the chi-squared statistic for cell A, we need to calculate (O - E)^2/E, where O is the observed frequency and E is the expected frequency for that cell. The expected frequency is calculated by multiplying the row total and column total for that cell and then dividing by the overall sample size.For cell A, the observed frequency is 7, the row total is 28, the column total is 30, and the sample size is 400. So the expected frequency is (28*30)/400 = 2.1.Therefore, the contribution to the chi-squared statistic for cell A is (7 - 2.1)^2/2.1 = 14.6.The total chi-squared statistic is the sum of the contributions from all cells, which is 72.6.The degrees of freedom for this test are (r-1)*(c-1) = (2-1)*(3-1) = 2.The p-value for the test can be found using a chi-squared distribution with 2 degrees of freedom.

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