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.

dc=6 square root of 3 and ac is 12 square root 3

c and d

step-by-step explanation:

square root of 3/2 = 18/c

cross multiply to get 18*2=√3*c

36/√3 * √3/√3 = c

c= 36*√3/3

c=12√3

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2