Question 1

A researcher compares the mean cholesterol levels between two groups: one taking a new medication and one taking a placebo. The 95% confidence interval for the difference in means is $$[2.1, 8.7]. $$What does this confidence interval suggest?

Accepted Answer

The mean cholesterol level for the medication group is significantly greater than the placebo group, with the true difference likely between 2.1 and 8.7.

Question 2

Which of the following is NOT part of the 5-number summary for a data set?

Accepted Answer

Mean

Question 3

Given the data set: $$2, 4, 7, 10, 15$$, what is the median?

Accepted Answer

$$7$$

Question 4

Which of the following best defines a parameter?

Accepted Answer

A numerical measurement describing a characteristic of a population.

Question 5

A fair die is rolled twice. What is the probability of getting a 6 on both rolls? (Use the multiplication rule for independent events.)

Accepted Answer

$$\frac{1}{36}$$

Question 6

Which of the following statements about the correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two quantitative variables.

Question 7

A sample of home prices contains several extremely high values. Which measure of center is most affected by these outliers?

Accepted Answer

Mean

Question 8

Which of the following is the correct symbolic form for the null and alternative hypotheses for testing if the mean weight of apples is less than 150g?

Accepted Answer

$$H_0$$: \mu = 150$$, H_a$$: \mu \u003c 150$$

Question 9

A data value is 2 standard deviations above the mean. What is its $$z-$$score?

Accepted Answer

$$z = 2$$

Question 10

Which of the following is a Type I error?

Accepted Answer

Rejecting a true null hypothesis.

Question 11

A survey asks every 10th person entering a hospital about their satisfaction. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 12

Which of the following is a discrete random variable?

Accepted Answer

The number of cars passing through a toll booth in an hour.

Question 13

If the variance of a data set is $$16$$, what is the standard deviation?

Accepted Answer

$$4$$

Question 14

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

Accepted Answer

The probability of success changes from trial to trial.

Question 15

A bag contains 5 red and 7 blue marbles. If two marbles are drawn without replacement, are the events independent?

Accepted Answer

No, because the probability changes after the first draw.

Question 16

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

Accepted Answer

$$E = z_{\alpha/2} \cdot \frac{\sigma}{\sqrt{n}}$$

Question 17

Which of the following best describes a sampling distribution?

Accepted Answer

The distribution of a statistic (like the mean) calculated from all possible samples of a given size from a population.

Question 18

A researcher wants to test if a new teaching method improves test scores. Which type of hypothesis test should be used?

Accepted Answer

A right-tailed test for the mean.

Question 19

Which of the following is TRUE about the use of a regression line to predict $$y$$ values?

Accepted Answer

It is appropriate only when the correlation is strong and the $$x$$ value is within the range of observed data.

Question 20

A student wants to know how many different ways 4 books can be arranged on a shelf. Which counting principle should be used?

Accepted Answer

Permutation

Comprehensive Statistics Study Guide: Step-by-Step Guidance

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