Asked by Claire Liang on Jul 13, 2024
Verified
In 2011,the student body of a state university in Alabama consists of 30% freshmen,25% sophomores,27% juniors,and 18% seniors.A sample of 400 students taken from the 2012 student body showed that there are 138 freshmen,88 sophomores,94 juniors,and 80 seniors.Test with 5% significance level to determine whether the student body proportions have changed.
Student Body Proportions
The distribution of various characteristics (e.g., gender, major, year) within a school's student population, often analyzed in educational studies.
Chi-squared Goodness-of-fit Test
A statistical test used to determine whether an observed distribution differs from an expected distribution.
Significance Level
The odds of wrongly rejecting the null hypothesis in statistical research, often indicated by the letter alpha.
- Absorb the methodology and interpretation of chi-squared goodness-of-fit tests.
- Uncover critical values and assess the findings of chi-squared tests.
- Draft null and alternative hypotheses for conducting goodness-of-fit tests.
Verified Answer
MA
Michael AlemuJul 15, 2024
Final Answer :
H0: p1 = .30,p2 =.25,p3 = 0.27,p4 = .18 H1: At least one proportion differs from their specified values Rejection region: χ2 > χ2.05,3 = 7.815 Test statistic: χ2 = 6.844 Conclusion: Cannot reject the null hypothesis.The student body proportions have not changed since 2011,according to the data.
Learning Objectives
- Absorb the methodology and interpretation of chi-squared goodness-of-fit tests.
- Uncover critical values and assess the findings of chi-squared tests.
- Draft null and alternative hypotheses for conducting goodness-of-fit tests.