8. Chi-square test on proportions Aa Aa A school district is conducting a study

Question

8. Chi-square test on proportions Aa Aa A school district is conducting a study to determine the relationship between high school student attendance and academic performance. Student attendance is classified as either Normal or Low, and student performance is classified as either Positive (average or higher) or Negative (below average). Out of the 4,342 students in the Normal attendance group, 52% showed Positive performance. Out of the 1,312 in the Low attendance group, 48% showed Positive performance. Fill in the following contingency table with the observed frequencies. Round your entries to the nearest integer Performance Total Attendance PositiveNegative Normal Low Total Complete the following table of expected frequencies. Round your entries to the nearest integer.

Explanation / Answer

Null HYpothesis : H0 : High school student attendence and academic performance are independent of each other.

Alternative HYpothesis : Ha : High school student attendence and academic performance are dependent of each other.

Contingency table with Observed Frequency

Expected Frequency

Value of CHi - square

X2 = (2258 - 2171)2/ 2171 +   (2084 - 2171)2/ 2171 + (630 - 656)2/ 656 + (682 - 656)2/656 = 9.05

alpha = 0.05, X2crit. = 3.8414

so X2 > X2crit. so we shall reject thenull hypothesis. We should conclude that there is significant relationship between student attendence and academic performance.

Performance Attendence Positive Negative Total Normal 2258 2084 4342 Low 630 682 1312 Total 2888 2766 5654

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