An online retailer employs 1,300 employees. one of their competitors would like to test the hypothesis that the average age of these 1,300 employees is less than 36 years old. a random sample of 22 employees was found to have an average age of 33.9 years. the standard deviation for this sample was 4.1 years. the competitor would like to set alphaαequals=0.025. what is the correct hypothesis statement for this hypothesis test?

Null hypothesis:  

Alternative hypothesis:  

Since the we can reject the null hypothesis at 2.5 % of significance.  

Step-by-step explanation:

Data given and notation  

represent the sample mean  

represent the standard deviation for the sample  

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses to be tested  

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

Null hypothesis:  

Alternative hypothesis:  

Compute the test statistic  

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

(1)  

t-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".  

We can replace in formula (1) the info given like this:  

Now we need to find the degrees of freedom for the t distirbution given by:

What do you conclude? Use the p-value approach  

Since is a one left tailed test the p value would be:  

Since the we can reject the null hypothesis at 2.5 % of significance.  

The slopes are the opposite and reciprocal

Step-by-step explanation:

The Slope of a Line

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

We need to prove lines RS and VU of the figure have the opposite and reciprocal slope, i.e., the lines are perpendicular.

Finding the coordinates of the points from the image:

R=(-2,5) S=(-5,2) V=(5,2) U=(2,5)

The slope of the line RS is:

The slope of line VU is:

Since:

The slopes are the opposite and reciprocal