Question

Zachary wondered how many text messages he sent on a daily basis over the past four years. He took an SRS
(simple random sample) of 50 days from that time period and found that he sent a daily average of 2 = 22.5
text messages. The daily number of texts in the sample were strongly skewed to the right with many outliers.
He's considering using his data to make a confidence interval for his mean number of daily texts over that entire
time period.
Which conditions for constructing a t interval have been met?
Choose all answers that apply:
The data is a random sample from the population of interest.
The sampling distribution of 2 is approximately normal.
Individual observations can be considered independent.

Answer 1

Using the Central Limit Theorem, it is found that the condition for constructing a confidence interval that has been met is:

The sampling distribution is approximately normal.

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 underlying distribution is skewed, however, the sample size is of 50 > 30, hence the condition that requires the sampling distribution to be normal is met.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Answer 2

Answer:

A, B, and C are correct