Final answer:
To compare the sleep times between teenagers and adults, we can use a t-test to determine if there is a significant difference in their means. First, calculate the t-value using the given information and then compare it to the critical value from a t-distribution table.
Step-by-step explanation:
In this question, we are given the mean and standard deviation of sleep times of a sample of 16 teenagers and a sample of 12 adults. We need to determine if teenagers sleep more than adults on average. To compare the sleep times between the two groups, we can use a t-test. A t-test is a statistical test that helps us determine if there is a significant difference between the means of two groups.
First, we calculate the t-value using the formula: t = (mean1 - mean2) / sqrt((s1^2 / n1) + (s2^2 / n2)), where mean1 and mean2 are the means of the two groups, s1 and s2 are the standard deviations, and n1 and n2 are the sample sizes.
Then, we compare the t-value to the critical value from a t-distribution table with the degrees of freedom (df) calculated using the formula: df = n1 + n2 - 2. If the t-value is greater than the critical value (depending on the desired level of significance, such as 0.05 or 0.01), we can conclude that there is a significant difference in the average sleep times between teenagers and adults.