Question

When testing a hypothesis about a single mean, a sample size of 200 is selected from a normally distributed population. If the population standard deviation is known, the correct test statistic to use is ___________.

Answer 1

Answer:

Null hypothesis:$\mu \leq \mu_o$  

Alternative hypothesis:$\mu > \mu_o$  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Step-by-step explanation:

Data given and notation  

$\bar X$ represent the sample mean

$\sigma$ represent the population standard deviation for the sample  

$n=200$ sample size  

$\mu_o$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

$p_v$ represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is equal to $\mu_o$, the system of hypothesis would be:  

Null hypothesis:$\mu \leq \mu_o$  

Alternative hypothesis:$\mu > \mu_o$  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".