Question

Is the confidence interval affected by the fact that the data appear to be from a population that is not normally​ distributed? A. ​Yes, because the sample size is not large enough. B. ​No, because the population resembles a normal distribution. C. ​Yes, because the population does not exhibit a normal distribution. D. ​No, because the sample size is large enough.

Answer 1

Answer:

D. No, because the sample size is large enough.

Step-by-step explanation:

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

If the sample size is higher than 30, on this case the answer would be:

D. No, because the sample size is large enough.

And the reason is given by The Central Limit Theorem since states if the individual distribution is normal then the sampling distribution for the sample mean is also normal.

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

If the sample size it's not large enough n<30, on that case the distribution would be not normal.