Question 1

Which of the following best describes the meaning of probability in the context of long-run frequency?

Accepted Answer

Probability is the proportion of times an outcome would occur in a very long sequence of observations.

Question 2

A random variable $$X is $$said to be discrete if:

Accepted Answer

It can take on only separate, distinct values such as $$0, 1, 2, \ldots$$

Question 3

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

The normal distribution is always skewed to the right.

Question 4

Suppose the mean number of hours college students sleep per night is $$\mu = 7$$ with a standard deviation $$\sigma = 1.5. $$What is the $$z-$$score for a student who sleeps 10 hours?

Accepted Answer

$$z = \dfrac{10 - 7}{1.5} = 2$$

Question 5

A 95% confidence interval for a population mean is constructed as $$\bar{x} \pm 2 	imes SE. $$What does the 95% confidence level mean?

Accepted Answer

If we repeated the sampling process many times, about 95% of the intervals would contain the true population mean.

Question 6

Which of the following is NOT an assumption required for most statistical significance tests?

Accepted Answer

The population must be divided into equal groups.

Question 7

A researcher wants to estimate the proportion of voters who support a new policy. She surveys a random sample and finds that 60% support the policy. Which of the following is the point estimate for the population proportion?

Accepted Answer

0.60

Question 8

Which of the following best describes the null hypothesis ($$H_0) in a $$statistical test?

Accepted Answer

It is the claim that is initially assumed to be true about the population parameter.

Question 9

In a chi-squared test of independence using a contingency table, what does a significant result indicate?

Accepted Answer

There is evidence that the two categorical variables are statistically dependent.

Question 10

Which of the following is a correct interpretation of a $$p-$$value in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.

Question 11

A sample mean is used to estimate the population mean. What property makes the sample mean an unbiased estimator?

Accepted Answer

Its sampling distribution is centered around the true population mean.

Question 12

Which of the following is TRUE about the Empirical Rule for normal distributions?

Accepted Answer

Approximately 95% of data falls within two standard deviations of the mean.

Question 13

A 99% confidence interval for a population mean will be ______ compared to a 95% confidence interval, assuming the same data.

Accepted Answer

Wider, because a higher confidence level requires a larger margin of error.

Question 14

Which estimation method involves resampling with replacement from the observed data to estimate the distribution of a statistic?

Accepted Answer

Bootstrap

Question 15

A hospital administrator wants to know if satisfaction with hospital services differs by age group. Which statistical tool is most appropriate to summarize the relationship between these two categorical variables?

Accepted Answer

A contingency table

Question 16

If a sample proportion is $$\hat{p} = 0.73$$ with a margin of error of $$0.02$$, what is the 95% confidence interval for the population proportion?

Accepted Answer

$$0.71 to$$ $$0.75$$

Question 17

Which of the following best describes statistical independence between two categorical variables?

Accepted Answer

The conditional distributions of one variable are identical for each category of the other variable.

Question 18

A researcher tests $$H_0$$: \mu = 50$$ versus H_a$$: \mu 
eq 50$$ using a sample mean of 54$, sample standard deviation s = 4$, and sample size n = 16$. What is the value of the test statistic?

Accepted Answer

$$z = \dfrac{54 - 50}{4/\sqrt{16}} = 4$$

Question 19

Which of the following is an example of an ordinal variable?

Accepted Answer

Opinion on government action: less, the same, more

Core Concepts in Probability, Distributions, Estimation, Hypothesis Testing, and Categorical Data Analysis

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