Question

If we believe the Central Limit Theorem is going to be accurate (and assuming the data were collected in a random fashion), we can perform a hypothesis test to test the claim that the population mean petal length is 1.3 centimeters. Is this claim reasonable, or do the data suggest instead that the mean is larger than 1.3 cm? Assume that the standard deviation of setosa petal length is 0.5 cm.

What is the theoretical standard deviation of the distribution of sample means under the null hypothesis (i.e., when H₀ is true)? Round to 3 decimals.

Answer 1

Let n shows the sample size. It is given that population standard deviation is

$\sigma=0.5$

The theoretical standard deviation of the distribution of sample means under the null hypothesis is

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{0.5}{\sqrt{n}}$

For example: If n=50 then

$\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{0.5}{\sqrt{50}}\approx 0.071$