The average student loan debt is reported to be $25,235. A student belives that the student loan debt is higher in her area. She takes a random sample of 100 college students in her area and determines the mean to be $27,524 and the standard devition to be $6000. Is there sufficient evidence to support the student' claim at a 5% significance level?

We reject the students claim because the P-value is less than the significance level.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = 25,235

Alternative hypothesis;Ha; μ > 25,235

Now, let's find the test statistic. Formula is;

t = (x' - μ)/(σ/√n)

We are given;

x' = 27,524

μ = 25,235

σ = 6000

n = 100

Thus;

t = (27524 - 25235)/(6000/√100)

t = 2289/600

t = 3.815

So from online p-value calculator as attached, using t=3.815, DF = 100-1 = 99 and significance level of 0.05, the P-value is gotten as p = 0.000237.

The p-value is less than the significance level of 0.05. Thus,we reject the students claim.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

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.