jayjay2006
09.04.2021 •
Mathematics
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.
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Ответ:
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.
Ответ:
To find this start with the original:
A = B + C/D ---> Subtract B from both sides
A - B = C/D ---> Multiply both sides by D
D(A-B) = C