At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 years. The population standard deviation is known to be 3.5 years. Determine whether or not the average age of the evening students is significantly different from 21. Use a 0.1 level of significance.

When we compare the significance level we see that so we can reject the null hypothesis at 10% of significance. So the  the true mean is difference from 21 at this significance level.

Step-by-step explanation:

Data given and notation  

represent the sample mean

represent the population standard deviation

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

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 average age of the evening students is significantly different from 21, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

 (1)  

Calculate the statistic

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

P-value

Since is a two sided test the p value would be:  

Conclusion  

When we compare the significance level we see that so we can reject the null hypothesis at 10% of significance. So the  the true mean is difference from 21 at this significance level.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.