Question

Zappos is an online retailer based in Nevada and employs 1,300 employees. One of their competitors, Amazon, would like to test the hypothesis that the average age of a Zappos employee is less than 36 years old. A random sample of 22 Zappos employees was found to have an average age of 33.9 years. The standard deviation for this sample was 4.1 years. Amazon would like to set α = 0.025. The conclusion for this hypothesis test would be that because the test statistic is

Answer 1

Answer:

$t=\frac{33.9-36}{\frac{4.1}{\sqrt{22}}}=-2.402$    

$df = n-1= 22-1=21$

$t_{\alpha/2}= -2.08$

Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old

Step-by-step explanation:

Data given

$\bar X=33.9$ represent the sample mean

$s=4.1$ represent the sample standard deviation

$n=22$ sample size  

$\mu_o =26$ represent the value that we want to test

$\alpha=0.025$ 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)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is less than 36 years old, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 36$  

Alternative hypothesis:$\mu < 36$  

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$  (1)  

And replacing we got:

$t=\frac{33.9-36}{\frac{4.1}{\sqrt{22}}}=-2.402$    

Now we can calculate the critical value but first we need to find the degreed of freedom:

$df = n-1= 22-1=21$

So we need to find a critical value in the t distribution with df =21 who accumulates 0.025 of the area in the left and we got:

$t_{\alpha/2}= -2.08$

Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old