Question 1

A 95% confidence interval for the difference in means between two populations is $$(-2.1, 4.3). $$What does this interval suggest about the difference in population means?

Accepted Answer

There is no significant difference between the two population means at the 95% confidence level.

Question 2

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

Accepted Answer

Mean

Question 3

Given a data value $$x = 85$$, a mean $$\mu = 70$$, and a standard deviation $$\sigma = 5$$, what is the $$z-$$score, and is this value significant at the 5% level (two-tailed)?

Accepted Answer

$$z = 3$$, which is significant since $$|z| \u003e 1.96$$

Question 4

Which of the following best defines a parameter?

Accepted Answer

A numerical measurement describing a characteristic of a population.

Question 5

A grouped frequency distribution table has class limits 10-19, 20-29, 30-39, etc. What is the class width?

Accepted Answer

$$10$$

Question 6

Which of the following is a correct symbolic representation for testing the claim 'the mean is greater than 50'?

Accepted Answer

$$H_0$$: \mu = 50$$, H_a$$: \mu \u003e 50$$

Question 7

Which of the following is NOT a type of probability distribution?

Accepted Answer

Binomial coefficient

Question 8

A researcher wants to estimate the average cholesterol level in adults. She divides the city into blocks and randomly selects some blocks, then surveys all adults in those blocks. What type of sampling is this?

Accepted Answer

Cluster sampling

Question 9

Which of the following statements about correlation is TRUE?

Accepted Answer

A correlation coefficient close to $$0$$ indicates little or no linear relationship.

Question 10

Which of the following is a Type I error?

Accepted Answer

Rejecting the null hypothesis when it is actually true.

Question 11

A hospital records the blood types of 1000 patients. What is the level of measurement for blood type?

Accepted Answer

Nominal

Question 12

If a data set contains several large outliers (such as home prices), which of the following is most likely true?

Accepted Answer

The mean will be greater than the median.

Question 13

A fair die is rolled twice. What is the probability of getting a 6 on both rolls?

Accepted Answer

$$\dfrac{1}{36}$$

Question 14

Which of the following best defines a sampling distribution?

Accepted Answer

The probability distribution of a statistic based on all possible samples of a specific size from a population.

Question 15

Given a variance $$s^2 = 25$, what is the standard deviation s$?

Accepted Answer

$$5$$

Question 16

A study finds a correlation coefficient $$r = 0.95$$ between hours studied and exam scores. Which statement is most accurate?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 17

A sample of 5 numbers: $$2, 4, 7, 10, 12. $$What is the median?

Accepted Answer

$$7$$

Question 18

Which of the following is a discrete random variable?

Accepted Answer

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

Question 19

A bag contains 5 red balls and 3 blue balls. If two balls are drawn without replacement, what is the probability both are red?

Accepted Answer

$$\dfrac{5}{8} 	imes \dfrac{4}{7} = \dfrac{20}{56} = \dfrac{5}{14}$$

Question 20

A confidence interval for a mean is $$(45, 55). $$What is the margin of error $$E$$?

Accepted Answer

$$E = \dfrac{55 - 45}{2} = 5$$

Comprehensive Statistics Study Guide: Step-by-Step Guidance

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