Question

In the following cases, each sample is from an SRS and the corresponding population has no outliers. Given the sample mean xˉ

and population standard deviation σ, judge whether in each case the sample size n is large enough to perform a hypothesis test. If not, add an assumption so that we could perform hypothesis tests
. a. Data from Normal distribution and n=3;

Answer 1

To perform a hypothesis test with a sample size of 3, we can assume that the population is approximately normally distributed.

Step-by-step explanation:

In order to perform a hypothesis test for a single population mean, the sample size needs to be sufficiently large or the population needs to be approximately normally distributed. In this case, the sample is from a normal distribution and the sample size is 3. A sample size of 3 is considered small, so we would not be able to perform the hypothesis test directly.

However, we can make an assumption that the population is approximately normally distributed even for smaller sample sizes. This is based on the Central Limit Theorem, which states that for a sufficiently large sample size, the distribution of the sample mean approaches a normal distribution.

Therefore, if we assume that the population is approximately normally distributed, we can still perform a hypothesis test with a sample size of 3.