Create a one sample t-test comparing the

age of the general population of college
students in traditional on-ground universities. Assume the population mean is 21. The numbers are 15, 16, 14, 13, 12,
17, 18,19,11, and 10.

http://en.wikipedia.org/wiki/Student's_t-test

To perform a one sample t-test comparing the age of the general population of college students in traditional on-ground universities, you need to follow these steps:

Step 1: State the Hypotheses
- Null Hypothesis (H0): The population mean age is equal to 21.
- Alternative Hypothesis (H1): The population mean age is not equal to 21.

Step 2: Set the Significance Level
Choose a significance level (commonly denoted as alpha) to determine the threshold for rejecting the null hypothesis. Let's assume a significance level of 0.05 (5%).

Step 3: Calculate the Sample Mean
Find the mean age of the given sample. In this case, the sample consists of the following ages: 15, 16, 14, 13, 12, 17, 18, 19, 11, and 10.

Sum = 15 + 16 + 14 + 13 + 12 + 17 + 18 + 19 + 11 + 10 = 145
Sample Mean = Sum / Sample Size = 145 / 10 = 14.5

Step 4: Calculate the Sample Standard Deviation
Find the standard deviation of the sample. This measures the spread of the data. To do this, you can use the formula for sample standard deviation:

Sample Deviation = sqrt[(Sum(x - mean)^2) / (n - 1)]

Where:
- Sum(x - mean)^2 is the sum of the squared differences between each value and the sample mean.
- n is the sample size.

For the given sample, the calculations would be as follows:

Sum([(15-14.5)^2 + (16-14.5)^2 + (14-14.5)^2 + (13-14.5)^2 + (12-14.5)^2 + (17-14.5)^2 + (18-14.5)^2 + (19-14.5)^2 + (11-14.5)^2 + (10-14.5)^2]) = 45

Sample Standard Deviation = sqrt(45 / (10 - 1)) = sqrt(45 / 9) = sqrt(5) ≈ 2.236

Step 5: Calculate the Test Statistic
The test statistic for a one-sample t-test is calculated using the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

For the given data, the calculations would be:

t = (14.5 - 21) / (2.236 / sqrt(10)) ≈ -10.56

Step 6: Determine the Critical Value
The critical value defines the cutoff point for rejecting the null hypothesis. The critical value can be obtained from the t-distribution table or using statistical software. Assuming a significance level of 0.05 and a two-tailed test (to consider both directions), the critical value for a sample size of 10 can be found.

Step 7: Make a Decision
Compare the test statistic (t-value) with the critical value to make a decision.

If the test statistic falls within the critical region (outside the range defined by the critical values), the null hypothesis is rejected. Otherwise, if the test statistic falls within the non-critical region, we fail to reject the null hypothesis.

In this case, since the t-value is extreme and falls in the critical region, we would reject the null hypothesis and conclude that the population mean age of college students in traditional on-ground universities is significantly different from 21.