Question

Question 1

We want to conduct a statistical test to determine how a sample mean compares to a population mean. We have alpha = 0.05. We have 40 observations in the sample, and our sample is normally distributed. We do not know our population standard deviation. Which test would we use?

Group of answer choices

a) z-test

b) t-test

Question 2

I want to see if the mean midterm scores for our class (the sample) differs from a baseline average of 75. What type of one-sample t test would I conduct?

Group of answer choices

a) one-tailed

b) two-tailed

Question 3

I conduct the t-test comparing the mean midterm score of our class (the sample) to the baseline null hypothesis mean of 75. I find that the difference between the mean of our class and the null hypothesis mean is statistically significant. I calculate Cohen's d to determine the effect size, and the resulting value is 0.012. What does this tell us about the statistical and substantive significance of this result?

Group of answer choices

a) The difference is not statistically significant or substantively significant.

b) There is a statistically significant, but not substantively significant difference.

c) There is a statistically significant and substantively significant difference.

Question 4

Which of the following has greater power, a one-tailed or two-tailed one-sample t-test?

Group of answer choices

a) they're the same

b) one-tailed

c) two-tailed

Question 5

If the standard error of an estimate is increased, what is the effect to the width of the confidence interval?

Group of answer choices

a) it gets wider

b) no change

c) it narrows

Question 6

In the most recent YouGov poll 28% of respondents supported Biden for the Democratic nominee. There were 722 respondents in the poll. What is the sample standard error for preference for Biden?

You have enough information to calculate this.

Question 7

Using the SE you calculated in the previous question, determine if the 28% support for Biden in the YouGov poll is significantly different than the national support for Biden that sits at 18.1%.

Use the critical t-value of +/- 1.96.

Show your work for the calculations and explain your answer.

Answer 1

1) Option - b) t-test

Since the population standard deviation is unknown and the population is normally distributed.

2) Option - b) two - tailed

3) Option - C) There is statistically significant and substantively significant difference.

4) Option - b) one-tailed

5) Option - a) It gets wider

As the standard error increases, the margin of error also increases. So that the width of the confidence interval becomes wider.

6) n = 0.28

   p = 722

SE = sqrt((1 - )/n)

      = sqrt(0.28(1 - 0.28)/722)

      = 0.0167

7) The confidence interval is

+/- z^* * SE

= 0.28 +/- 1.96 * 0.0167

= 0.28 +/- 0.0327

= 0.2473, 0.3127

Since 0.181 does not lie in the confidence interval, So we can conclude that the 28% support for Biden in the YouGov poll is significantly different than the national support for Biden that sits at 18.1%.