Question

Is there a difference in the amount of time spent volunteering between freshman and seniors? one hundred freshman and one hundred seniors were asked how many hours they had spent volunteering in the past month. what type of test would they conduct to test this claim?

Answer 1

To test whether there is a difference in volunteer time between freshman and seniors, an independent samples t-test is used. The process involves formulating hypotheses, choosing a significance level, calculating a t-statistic, and comparing it to a critical t-value to decide on the null hypothesis.

Step-by-step explanation:

To determine if there is a difference in the amount of time spent volunteering between freshman and seniors, a statistical hypothesis test can be conducted. The appropriate test for this scenario is an independent samples t-test, which is used to compare the means of two separate groups to see if there is a significant difference between them. This test would be conducted under the assumption that the data follows a normal distribution and has equal variances (or use a version of the test that adjusts for unequal variances).

The steps for conducting this t-test are as follows:

1. Formulate the null hypothesis (H0: µ1 = µ2) which states that there is no difference in the mean hours of volunteering between the two groups.
2. Formulate the alternative hypothesis (Ha: µ1 ≠ µ2), indicating that there is a difference.
3. Choose a significance level (commonly α = 0.05).
4. Calculate the t-statistic based on the sample data.
5. Determine the critical t-value from the t-distribution table based on the degrees of freedom and the chosen α.
6. Compare the calculated t-statistic with the critical t-value to decide whether to reject the null hypothesis.

If the null hypothesis is rejected, it suggests that there is a statistically significant difference in the amount of time spent volunteering between freshman and seniors.

Answer 2

There is a difference in the amount of time spent volunteering between fresh man and seniors. The type of test suitable for testing this claim is called two proportion z test. This test is suitable because, simple random method was used for sampling, the samples were independent, each population was at least ten times bigger than the samples and each sample included at least ten failures and ten successes.