Researchers doing a study comparing time spent on social media and time spent on studying randomly sampled 200 students at a major university. They found that students in the sample spent an average of 2.3 hours per day on social media and an average of 1.8 hours per day on studying. If all the students at the university in fact spent 2.2 hours per day on studying, with a standard deviation of 2 hours, the sampling distribution of the time spent studying has approximate distribution

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Each student:

Mean of 2.2 hours, standard deviation of 2 hours.

Sampling distribution of the time spent studying has approximate distribution

Sample of 200.

By the Central Limit Theorem,

Approximately normal

Mean 2.2

Standard deviation [tex]s = \frac{2}{\sqrt{200}} = 0.1414[/tex]

The sampling distribution of the time spent studying has an approximately normal distribution, with mean 2.2 and standard deviation 0.1414.