Answer to Question #215339 in Statistics and Probability for floren

Question

What appropriate test statistic is used given the

sample size is 35 and sample standard deviation is 1.2?

Answer 1

When dealing with a large sample of size n >30 from a population which need not be normal but has finite variance, we can use the central limit theorem to justify using the test for normal populations. Even when $\sigma^2$ is unknown we can approximate its value with $s^2$ in the computation of the test statistic.

Test-statistic:

$Z= \frac{\bar{x} - \mu}{s/ \sqrt{n}}$

$\bar{x} =$ sample mean

$\mu =$ population mean

s = sample standard deviation

n = sample size