In: Statistics and Probability
Directions Use the Crosstabs option in the Descriptives menu to answer the questions based on the following scenario. (Be sure to select Chi-square from the Statistics submenu and Observed, Expected, Row, and Column in the Cells submenu. Assume a level of significance of .05).
Scenario
The school district recently adopted the use of e-textbooks, and the superintendent is interested in determining the level of satisfaction with e-textbooks among students and if there is a relationship between the level of satisfaction and student classification. The superintendent selected a sample of students from one high school and asked them how satisfied they were with the use of e-textbooks. The data that were collected are presented in the following table
Satisfied
Yes: Freshman (23) Sophmore (21) Junior (15) Senior (8)
No: Freshman (8) Sophmore (4) Junior (15) Senior (24)
Questions:
1. Of the students that were satisfied, what percent were Freshmen, Sophomore, Junior, and Senior? (Round your final answer to 1 decimal place).
2. State an appropriate null hypothesis for this analysis.
3. What is the value of the chi-square statistic?
4. What are the reported degrees of freedom?
5. What is the reported level of significance?
6. Based on the results of the chi-square test of independence, is there an association between e-textbook satisfaction and academic classification?
7. 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 the analysis.
#1)
Percentages of Freshmen, Sophomore, Junior, and Senior that were satisfied are
Freshmen = 23/67 = 34.3%
Sophomore = 21/67 = 31.3%
Junior = 15/67 = 22.4%
Senior = 8/67 = 11.9%
#2) Null and alternative hypotheses :
H0 : The variables level of satisfaction and student classification is independent.
Ha : The variables level of satisfaction and student classification is not independent.
#3) chi square statistic:
Observed frequency table :
We need to find expected frequency.
Expected frequency =
For example expected frequency for satisfied and Freshmen = 67*31/118 = 17.6017
Expected frequency table :
χ2 = ; O is observed and E is expected frequency.
χ2 = 25.1103
#4 )
Degrees of freedom (df) = (r-1)(c-1) r is level of satisfaction and c is categories of students.
r = 2 and c = 4
df = (2-1)*(4-1) = 1*3 = 3
df = 3
#5) We are given level of significance α = 0.05
Therefore critical value χ2(0.05,3) = 7.815 -------- ( From chi square table )
#6)
Decision : As χ2 = 25.1103is greater than χ2(0.05,3) = 7.815
We reject H0,
Conclusion: We have significant evidence that there is a relationship between the level of satisfaction and student classification.