Math Problem Statement
Is there a difference between community college statistics students and university statistics students in what technology they use on their homework? Of the randomly selected community college students 68 used a computer, 84 used a calculator with built in statistics functions, and 24 used a table from the textbook. Of the randomly selected university students 43 used a computer, 77 used a calculator with built in statistics functions, and 38 used a table from the textbook. Conduct the appropriate hypothesis test using an = 0.05 level of significance.
What is the correct statistical test to use? Homogeneity Goodness-of-Fit Paired t-test Independence
What are the null and alternative hypotheses?
Type of student and type of technology used for statistics homework are dependent. The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework. Type of student and type of technology used for statistics homework are independent. The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
Type of student and type of technology used for statistics homework are independent. The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework. The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
Solution
Correct Statistical Test
The appropriate statistical test to use here is Homogeneity, because the goal is to compare the distributions of technology use across two different populations (community college and university students).
Null and Alternative Hypotheses
The null hypothesis () and the alternative hypothesis () are framed as follows:
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Null Hypothesis (): The distribution of the technology that community college statistics students use for their homework is the same as the distribution of the technology that university statistics students use for their homework.
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Alternative Hypothesis (): The distribution of the technology that community college statistics students use for their homework is not the same as the distribution of the technology that university statistics students use for their homework.
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Math Problem Analysis
Mathematical Concepts
Statistics
Chi-Square Test for Homogeneity
Hypothesis Testing
Formulas
Chi-square statistic formula: χ² = Σ((O - E)² / E), where O = Observed frequencies, E = Expected frequencies
Expected frequency formula: E = (Row total × Column total) / Grand total
Theorems
Chi-Square Distribution
Suitable Grade Level
Undergraduate Statistics
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