Q: A business analyst wants to compare the variability of two stocks, one priced in USD and one in EUR. Which measure should they use?

Coefficient of Variation ($$CV = \frac{S}{\overline{X}} \times 100\%)$$

Question 1

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

Accepted Answer

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

Question 2

Which of the following is NOT a property of the standard deviation?

Accepted Answer

It is always larger than the range.

Question 3

A business analyst wants to compare the variability of two stocks, one priced in USD and one in EUR. Which measure should they use?

Accepted Answer

Coefficient of Variation ($$CV = \frac{S}{\overline{X}} 	imes 100\%)$$

Question 4

Which sampling method divides the population into groups based on a characteristic, then randomly samples from each group?

Accepted Answer

Stratified sampling

Question 5

Given the following data set: 2, 4, 4, 4, 5, 5, 7, 9. What is the mode?

Accepted Answer

4

Question 6

Which of the following is TRUE about the median?

Accepted Answer

It can be used for both numerical and ordinal data.

Question 7

A company wants to estimate the average time (in minutes) customers spend on their website. They collect a sample of 100 customers and find a mean of 12 minutes with a standard deviation of 3 minutes. What is the standard error of the mean?

Accepted Answer

$$\frac{3}{\sqrt{100}} = 0.3$$

Question 8

Which of the following statements about the Central Limit Theorem (CLT) is correct?

Accepted Answer

The CLT states that the sampling distribution of the sample mean approaches normality as the sample size increases, regardless of the population's distribution.

Question 9

A survey asks 200 people if they prefer product A or B. 120 choose A. What is the sample proportion ($$\hat{p}) of $$people who prefer A?

Accepted Answer

$$\frac{120}{200} = 0.6$$

Question 10

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

Accepted Answer

The mean, median, and mode are all equal.

Question 11

If a dataset is left-skewed, which of the following is true?

Accepted Answer

Mean \u003c Median

Question 12

A company wants to know if a new training program increases sales. They collect sales data before and after the program for the same employees. Which statistical test is most appropriate?

Accepted Answer

Paired samples t-test

Question 13

Which formula would you use to calculate the probability of getting exactly 3 heads in 5 coin tosses (fair coin)?

Accepted Answer

$$P(X=3) = \binom{5}{3} (0.5)^3$ (0.5$$)^{2}$$

Question 14

Which of the following is NOT an assumption of simple linear regression?

Accepted Answer

The independent variable X must be categorical

Question 15

A regression analysis yields $$R^2 = 0.85$. What does this mean?

Accepted Answer

85% of the variation in Y is explained by the variation in X.

Question 16

Which formula is used to standardize a value X in a normal distribution?

Accepted Answer

$$Z = \frac{X - \mu}{\sigma}$$

Question 17

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

95% of all possible samples will produce intervals that contain the population mean.

Question 18

Which of the following is the formula for the variance of a sample?

Accepted Answer

$$s^2$$ = \frac{\sum (X - \overline{X}$$)^2$$}{n-1}$$

Question 19

A business wants to predict sales using both advertising spend and price as predictors. Which statistical method should they use?

Accepted Answer

Multiple linear regression

Business Statistics: Foundational Concepts and Descriptive Measures

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