Question

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 51 used a computer, 86 used a calculator with built in statistics functions, and 28 used a table from the book. Of the randomly selected university students 49 used a computer, 70 used a calculator with built in statistics functions, and 26 used a table from the book. Conduct the appropriate hypothesis test using an a = 0.05 level of significance.

a. What is the correct statistical test to use?
1. Homogeneity
2. Independence
3. Goodness-of-Fit
4. Paired t-test

Answer 1

The correct statistical test is the chi-square test for independence, used to examine if there's an association between the type of institution and the technology used by statistics students. This test uses the contingency table of observed frequencies and compares them to expected frequencies. A conclusion is reached based on whether the computed p-value is less than the significance level of 0.05.

Step-by-step explanation:

The correct statistical test to determine if there is a difference between the technology used by community college statistics students and university statistics students on their homework is the chi-square test for independence. This test compares the frequencies of category counts between the two independent groups to see if there's a significant association between the type of institution and the technology used. The null hypothesis is that there is no association between the type of institution and the technology used, meaning the distributions of technology used should be similar for both community college and university students.

Here are the steps for conducting the chi-square test for independence using the provided data:

1. Formulate the null and alternative hypotheses.
2. Calculate the expected frequencies for each cell in a contingency table.
3. Calculate the chi-square test statistic.
4. Compare the test statistic to the critical value from the chi-square distribution or calculate the p-value.
5. Make a decision to reject or not reject the null hypothesis based on the p-value and the significance level, α = 0.05.
6. Draw a conclusion based on the decision made in step 5.

Given an α of 0.05 and a decision to reject the null hypothesis, the conclusion is that there is sufficient evidence to suggest that the distribution of technology use for homework differs between community college and university statistics students.