Question

A website streams movies and television shows to millions of users. Employees know that the average time a user spends per session on their website is 2 hours. The website changed its design, and they wanted to know if the average session length was longer than 2 hours. They randomly sampled 100 users and found that their session lengths had a mean of 2.75 hours and a standard deviation of 1.55 hours. The employees want to use these sample data to conduct at test about the mean.
Required:
Which conditions for performing this type of test did their sample meet?

Answer 1

Using the Central Limit Theorem, it is found that since the sample size is greater than 30, a normal approximation can be used, hence the test can be made.

Central Limit Theorem

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

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

In this problem, the distribution of lengths is skewed, however, since the sample size is of 100 greater than 30, a normal approximation can be used, hence the test can be made.

To learn more about the Central Limit Theorem, you can check brainly.com/question/24663213