Question

A STAT 200 instructor wants to know if more than half of online students use the eTextbook.  Conduct a randomization test given that 80 students in a random sample of 120 use the eTextbook.

A. Determine what type of test you need to conduct and write the hypotheses.

B. Construct a randomization distribution under the assumption that the null hypothesis is true. Take at least 5000 resamples.

C. Use the randomization distribution to find the p-value.

D. Decide if you should reject or fail to reject the null hypothesis.

E. State a real-world conclusion in relation to the original research question.

Answer 1

A)

We have to determine type of test you need to conduct and write the hypotheses.

It is given that A STAT 200 instructor wants to know if more than half of online students use the e Textbook

It means >50%

there is given as one sample of stat 200 students

Given that 80 students in random sample of 120

We want to calculate  that if more than half of online students use the e Textbook

which will be >50%

Null hypothesis will be

Alternate hypothesis will be

b)

We have to construct the randomization distribution under the assumption that null hypothesis is true

Take at least 5000 re-samples

Let us first understand

We will use randomization distribution to determine how likely our sample statistic it is given that the null hypothesis is true.

This probability is known as the p-value. The p-value is the proportion of samples on the randomization distribution that are more extreme than our observed sample in the direction of the alternative hypothesis. T

he p-value is compared to the alpha level (typically 0.05).

Case 1:

If

then we fail to reject the null hypothesis and conclude that there is not evidence of a difference in the population.

This does not mean that the null hypothesis is true, it only means that we do not have sufficient evidence to say that it is likely false. These results are not statistically significant.

Case 2:

If

then we reject the null hypothesis and conclude that there is a difference in the population.

These results are statistically significant.

Randomization distribution is given as bleow using statkey of at least 5000 resamples

c)

p value is 0.49

d)

P>0.05

With the p value being more than the null hypothesis, we fail to reject the null hypothesis

e)

There is not evidence from the sample that more than half  of stat 200 students want to purchase the textbook