Question

College math instructors suggest that students spend 2 hours outside class studying for every hour in class. So, for a 4-unit math class, students should spend at least 8 hours (480 minutes) studying each week. A statistics instructor randomly selected students during the third week of the semesters, the number of minutes students spent on studying are recorded below. At 0.05 level of significance to test the claim that students are studying less than 480 minutes each week. Assume the data come from a population that is normally distributed.
504 267 220 322 538 542 428 481 413 302 602 150 247

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 480
Alternative Hypothesis: μ < 480

Rejection Region
This is left tailed test, for α = 0.05 and df = 12
Critical value of t is -1.782.
Hence reject H0 if t < -1.782

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (385.85 - 480)/(143.5919/sqrt(13))
t = -2.364

P-value Approach
P-value = 0.0179
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that students are studying less than 480 minutes each week.