A 20-question multiple choice quiz has five choices for each question. Suppose that a student just guesses, hoping to get a high score. The teacher carries out a hypothesis test to determine whether the student was just guessing. The null hypothesis is p = 0.20, where p is the probability of a correct answer. a. Which of the following describes the value of the z-test statistic that is likely to result? Explain your choice.

i. The z-test statistic will be close to 0.
ii. the z-test statistic will be far from 0.

b. Which of the following describes the p-value that is likely to result? Explain your choice.

i. The p-value will be small.
ii. The p-value will not be small.

a)  i. The z-test statistic will be close to 0, as the sample mean and the tested proportion are expected to be close values.

b)  ii. The p-value will not be small, as the z-statistic is close to 0.

Step-by-step explanation:

The null hypothesis is p = 0.20

The teacher carries out a hypothesis test to determine whether the student was just guessing.

Test if the proportion is different from 0.2. So the alternate hypothesis is:

Five choices for each question, one of which is correct.

Probability of having a correct answer is

The test statistic is:

In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.

a. Which of the following describes the value of the z-test statistic that is likely to result?

In this question, , which meas that the numerator of the z-statistic will be close to 0, which means that the z-test statistic will be close to 0.

b. Which of the following describes the p-value that is likely to result?

pvalue is 2 multiplied by the pvalue of Z(if negative), or 1 subtracted by the pvalue of Z(if positive).

Since the value of Z is close to 0, either the pvalue of Z or 1 subtracted by the pvalue of Z is close to 0.5, and multiplied by 2 will be close to 1. So, as Z is close to 0, the pvalue will not be small.

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".