Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical characteristic of a population, while a statistic describes a sample.

Question 2

A hospital administrator wants to estimate the average length of stay for patients after a Caesarean section. Which of the following is the best example of a sample in this context?

Accepted Answer

A randomly selected group of 100 patients who had a Caesarean section at the hospital last year.

Question 3

Which sampling method is most appropriate when a population is naturally divided into subgroups and you want to ensure each subgroup is represented?

Accepted Answer

Stratified random sampling

Question 4

A researcher measures the blood pressure of every 10th patient entering a clinic. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 5

Which of the following is NOT a property of the mean absolute deviation (MAD)?

Accepted Answer

It is always larger than the standard deviation for any data set.

Question 6

Given the data set: 2, 4, 6, 8, 10, what is the median?

Accepted Answer

6

Question 7

Which of the following statements about the empirical rule is correct for a mound-shaped (normal) distribution?

Accepted Answer

About 68% of observations fall within 1 standard deviation of the mean.

Question 8

If a data set has a mean of 50 and a standard deviation of 5, what is the Z-score for an observation of 60?

Accepted Answer

$$Z = \frac{60 - 50}{5} = 2$$

Question 9

Which of the following is true about percentiles?

Accepted Answer

The 50th percentile is also known as the median.

Question 10

A boxplot is most useful for which of the following purposes?

Accepted Answer

Identifying outliers and visualizing the spread of data.

Question 11

If a variable is transformed by $$y = 3x + 2$$, what is the new mean in terms of the original mean $$\bar{x}$$?

Accepted Answer

$$3\bar{x} + 2$$

Question 12

Which of the following best describes a mutually exclusive event?

Accepted Answer

Two events that cannot occur at the same time.

Question 13

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Question 14

Which formula correctly calculates the sample variance $$s^2$$ for a data set?

Accepted Answer

$$s^2$$ = \frac{\sum_{i=1}^{n} (x_i - \bar{x}$$)^2$$}{n-1}$$

Question 15

Which of the following is a correct application of Chebyshev's inequality for any data set?

Accepted Answer

At least $$1 - \frac{1}{k^2$} of $$the data values lie within $$k$$ standard deviations of the mean.

Question 16

In probability, what does the law of large numbers state?

Accepted Answer

As the number of trials increases, the proportion of times an event occurs approaches its theoretical probability.

Question 17

Which of the following is true about the difference between observational studies and experiments?

Accepted Answer

Experiments impose treatments and can establish causality, while observational studies only observe variables and cannot establish causality.

Question 18

A researcher wants to know if income is related to happiness. Which type of variable is 'income' in this study?

Accepted Answer

Explanatory variable

Question 19

Which of the following is the correct formula for the conditional probability of A given B?

Accepted Answer

$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Statistics Fundamentals: Introduction, Data Organization, Descriptive Measures, and Probability

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