Question 1

Which of the following best describes the type of distribution shown in the third image (quantile plot with points closely following a straight line)?

Accepted Answer

A normal distribution, because the points closely follow a straight line.

Question 2

Refer to the formula in the fifth image. What does the denominator $$(n-1)$$ represent in the calculation of the sample standard deviation?

Accepted Answer

It corrects for bias in the estimation of the population standard deviation.

Question 3

Which Stata command would you use to generate a histogram for a variable named 'height'?

Accepted Answer

hist height

Question 4

A researcher wants to estimate the average height of all university students. She divides the students into freshmen, sophomores, juniors, and seniors, then randomly samples from each group. What sampling method is she using?

Accepted Answer

Stratified sampling

Question 5

Which of the following is NOT a requirement for a binomial distribution?

Accepted Answer

The probability of success must change from trial to trial.

Question 6

A time-series graph is best used to:

Accepted Answer

Show how a variable changes over time.

Question 7

If a Z-score is calculated as $$z = \frac{x - \bar{x}}{s}$$ and the result is $$-2.5$$, what does this indicate about the value of $$x$$?

Accepted Answer

It is significantly lower than the mean.

Question 8

Which of the following is an example of a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 9

Given a sample mean of 50, a population standard deviation of 10, and a sample size of 100, what is the standard error of the mean?

Accepted Answer

$$\frac{10}{\sqrt{100}} = 1$$

Question 10

Which Stata command would you use to find the p-value for a two-tailed z-test if you have calculated a z-score?

Accepted Answer

di 2*(1 - normal(abs(z)))

Question 11

A frequency distribution has a minimum value of 75 and a maximum value of 324, and you want 5 classes. What is the class width?

Accepted Answer

$$(324 - 75) \div 5 = 49.8$$

Question 12

Which of the following best describes the main problem with a graph that uses a nonzero vertical axis?

Accepted Answer

It exaggerates differences between groups.

Question 13

If you want to calculate the probability of getting at least 3 successes in 10 independent trials with probability of success $$p = 0.2$$ per trial, which Stata command would you use?

Accepted Answer

display binomial(10, 3, 0.2)

Question 14

Which of the following is the correct formula for the mean of a binomial distribution?

Accepted Answer

$$\mu = np$$

Question 15

A sample of 20 students has test scores with a mean of 75 and a standard deviation of 10. What is the z-score for a student who scored 95?

Accepted Answer

$$z = \frac{95 - 75}{10} = 2$$

Question 16

Which of the following best describes a cluster sampling method?

Accepted Answer

Dividing the population into sections, randomly selecting some sections, and including all members from those sections.

Question 17

Which measure of center is most affected by outliers?

Accepted Answer

Mean

Question 18

A researcher collects data on the number of hours students study per week and their exam scores. Which graph would best display the relationship between these two variables?

Accepted Answer

Scatterplot

Question 19

Which of the following is the correct formula for the margin of error in a confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

$$E = z^* \frac{\sigma}{\sqrt{n}}$$

Introductory Statistics: Comprehensive Study Notes and Stata Commands

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