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 200 patients. What type of variable is blood type?

Accepted Answer

Qualitative nominal

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 statements about the normal distribution is TRUE?

Accepted Answer

The mean, median, and mode are all equal.

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

$$0.9$$

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 formula: $$P(X = k) = \binom{n}{k} p^k (1-p$$)^{n-k}$$)

Accepted Answer

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

Question 9

Which of the following is NOT a property of the Pearson correlation coefficient $$r$$?

Accepted Answer

It can be used to infer causation between variables.

Question 10

A researcher wants to estimate the average height of adult males in a city. Which sampling method is most appropriate to ensure 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 clinical trial with 50 patients, 35 are cured. Which test is appropriate to evaluate the company's claim?

Accepted Answer

Test of a single proportion

Question 14

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 15

In a simple linear regression, which method is 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 should be used?

Accepted Answer

Test for difference of means

Question 17

Which of the following is a property of the Poisson distribution?

Accepted Answer

Its mean and variance are equal.

Question 18

If $$X is a $$continuous random variable with probability density function $$f(x)$$, what is the probability that $$X$$ takes any specific value $$a$$?

Accepted Answer

$$0$$

Question 19

Which of the following is an example of a non-probabilistic sampling method?

Accepted Answer

Convenience sampling

Question 20

A company wants to estimate the proportion of defective products in a large shipment. Which of the following best describes the parameter of interest?

Accepted Answer

The proportion of defective products in the population

Basic Statistics: Course Syllabus and Core Concepts

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