Q: Suppose the mean weight of a sample of 25 apples is 150g with a standard deviation of 10g. What is the 95% confidence interval for the mean weight? (Assume normality and use $$z = 1.96)$$

$$150 \pm 1.96 \times \frac{10}{\sqrt{25}}$$

Q: Which of the following is the formula for the coefficient of variation (CV) of a sample?

$$CV = \frac{s}{\bar{x}} \times 100\%$$

Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population includes all elements of interest, while a sample is a subset selected from the population.

Question 2

A researcher records the blood types (A, B, AB, O) of 100 patients. What type of variable is blood type?

Accepted Answer

Qualitative (categorical) variable

Question 3

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

Accepted Answer

$$4$$

Question 4

Which of the following formulas correctly represents the variance $$s^2 of a $$sample of $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$ with sample mean $$\bar{x}$$?

Accepted Answer

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

Question 5

A fair die is rolled once. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{1}{3}$$

Question 6

Which of the following is an example of a continuous random variable?

Accepted Answer

The time (in seconds) it takes for a chemical reaction to complete.

Question 7

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.2$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.7$$

Question 8

A machine produces light bulbs with a 2% defect rate. If 10 bulbs are selected at random, what is the probability that exactly one bulb is defective? (Use the binomial distribution: $$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$)

Accepted Answer

$$\binom{10}{1} (0.02)^1$ (0.98)^9$

Question 9

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

Accepted Answer

Approximately 68% of the data falls within one standard deviation of the mean.

Question 10

A researcher wants to estimate the average height of adult males in a city. Which sampling method ensures every individual has an equal chance of being selected?

Accepted Answer

Simple random sampling

Question 11

Suppose the mean weight of a sample of 25 apples is 150g with a standard deviation of 10g. What is the 95% confidence interval for the mean weight? (Assume normality and use $$z = 1.96)$$

Accepted Answer

$$150 \pm 1.96 	imes \frac{10}{\sqrt{25}}$$

Question 12

Which of the following is the correct null hypothesis for testing whether the mean of a population is equal to 100?

Accepted Answer

$$H_0$$: \mu = 100$$

Question 13

A pharmaceutical company claims that its new drug cures 80% of patients. In a sample of 50 patients, 35 are cured. What is the sample proportion of cured patients?

Accepted Answer

$$0.70$$

Question 14

Which of the following best describes the Pearson correlation coefficient?

Accepted Answer

It measures the strength and direction of the linear relationship between two quantitative variables.

Question 15

In a simple linear regression, which method is commonly used to estimate the parameters of the regression line?

Accepted Answer

Method of least squares

Question 16

A hospital administrator wants to compare the average length of stay for patients in two different wards. Which statistical test is most appropriate?

Accepted Answer

Two-sample t-test for means

Question 17

Which of the following is the formula for the coefficient of variation (CV) of a sample?

Accepted Answer

$$CV = \frac{s}{\bar{x}} 	imes 100\%$$

Question 18

A quality control engineer inspects 100 items and finds 5 defective. If the probability of finding a defective item is 0.05, what is the expected number of defectives in 100 items?

Accepted Answer

$$100 	imes 0.05 = 5$$

Question 19

Which of the following is NOT a property of the Poisson distribution?

Accepted Answer

It is used for continuous random variables.

Question 20

A researcher wants to test if the variance of a population is equal to a specified value. Which test should be used?

Accepted Answer

Chi-square test for variance

Structured Study Guide: Basic Statistics (ESTATÍSTICA BÁSICA)

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