Question

The student academic group on a college campus claims that freshman students study at least $2.5$ hours per day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of $30$ freshman students and found a mean study time of $137$ minutes with a standard deviation of $45$ minutes. At $\alpha =0.01$ level, is the student academic group’s claim correct?

Short answer

We can conclude that on average, freshman students study for at least$2.5$hours or$150$minutes.

Step-by-step solution

Given information

The freshman students study at least$2.5$hours per day. The mean study time is$137$minutes with a standard deviation of$45$minutes.

Explanation

State the hypotheses:

The null hypothesis states that on average, freshman students study at least $2.5$hours or $150$minutes. In symbols:

$H_0:\mu \ge 150$

The alternative hypothesis states that on average, freshman students study less than $2.5$hours or $150$minutes. In symbols:

$H_0=\mu <150$

State the P-value:

$P-value=0.0622$

State alpha:

$a=0.01$

Since the null hypothesis is not rejected, we can conclude that on average, freshman students study for at least $2.5$hours or$150$minutes.