The average age of evening students at a local college has been 21.
A sample of 19 students was selected in order to determine whether the average age of students had increased.
The average age of the students in the sample was 23 with a standard deviation of 3.5. Determine whether or not there has been an increase in the average age of the evening students. Use a 0.1 level of significance.
Do you want P = 0.1 or .01?
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√(n-1)
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
To determine whether there has been an increase in the average age of the evening students, we can conduct a hypothesis test. Let's set up the null and alternative hypotheses:
Null hypothesis (H0): The average age of the evening students has not increased.
Alternative hypothesis (Ha): The average age of the evening students has increased.
Now, we can calculate the test statistic and compare it to the critical value to make a decision. Here are the steps:
Step 1: Set the significance level (α):
The significance level (α) is given as 0.1 or 10%.
Step 2: Calculate the test statistic:
We will use the t-test for a single sample. The formula for the test statistic is given by:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is 23, the population mean is 21, the sample standard deviation is 3.5, and the sample size is 19.
t = (23 - 21) / (3.5 / sqrt(19))
Step 3: Determine the critical value:
To determine the critical value, we need to find the degrees of freedom (df) and refer to the t-distribution table. Since this is a single-sample t-test, the degrees of freedom is equal to (sample size - 1). In this case, df = 19 - 1 = 18.
From the t-distribution table, we look up the critical value at a 0.1 level of significance for df = 18. Let's assume the critical value is t_crit.
Step 4: Make a decision:
If the absolute value of the test statistic is greater than the critical value (|t| > t_crit), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Now, you would need to find the critical value from the t-distribution table and compare it with the test statistic t to make a decision.