A researcher is interested in comparing the maturity level of students who volunteer versus those who don't.
Calculate the correct t-test.
Maturity scores for non-volunteers: 33, 41, 54, 13, 22, 26
Maturity scores for volunteers: 41, 48, 61, 72, 83, 55
https://sciencing.com/calculate-tscore-5135749.html
To calculate the correct t-test for comparing the maturity level of students who volunteer versus those who don't, we need to follow these steps:
Step 1: State the null hypothesis (H0) and the alternative hypothesis (Ha):
- Null Hypothesis (H0): There is no significant difference in the maturity level between students who volunteer and those who don't.
- Alternative Hypothesis (Ha): There is a significant difference in the maturity level between students who volunteer and those who don't.
Step 2: Determine the significance level (α) for the t-test. Typically, α is set at 0.05, indicating a 5% chance of rejecting the null hypothesis incorrectly.
Step 3: Collect the data for both groups:
- Maturity scores for non-volunteers: 33, 41, 54, 13, 22, 26
- Maturity scores for volunteers: 41, 48, 61, 72, 83, 55
Step 4: Calculate the sample means for both groups:
- Sample mean for non-volunteers (x̄1): Calculate the mean (average) of the non-volunteer maturity scores.
- Sample mean for volunteers (x̄2): Calculate the mean (average) of the volunteer maturity scores.
Step 5: Calculate the sample standard deviations for both groups:
- Sample standard deviation for non-volunteers (s1): Calculate the standard deviation of the non-volunteer maturity scores.
- Sample standard deviation for volunteers (s2): Calculate the standard deviation of the volunteer maturity scores.
Step 6: Determine the number of observations (n1 and n2) for each group:
- n1: Number of observations in the non-volunteer group
- n2: Number of observations in the volunteer group
Step 7: Compute the t-statistic using the formula:
t = (x̄1 - x̄2) / √((s1^2 / n1) + (s2^2 / n2))
Step 8: Calculate the degrees of freedom (df), which is equal to (n1 + n2 - 2).
Step 9: Look up the critical t-value from the t-distribution table using the significance level (α) and degrees of freedom (df).
Step 10: Compare the calculated t-statistic with the critical t-value. If the calculated t-statistic is greater than the critical t-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Performing these steps will give you the correct t-test for comparing the maturity level between students who volunteer and those who don't.