Question 1

A researcher wants to estimate the average time students spend on the internet per day. Which of the following is the most appropriate variable type for this measurement?

Accepted Answer

This variable is a continuous numerical variable that is interval-scaled.

Question 2

Suppose you toss a standard fair die. Let $A$ = {Die shows an odd number} and $B$ = {Die shows a number smaller than or equal to 3}. What is $P(A \cap B)$?

Accepted Answer

$1/3$

Question 3

A hospital reports that 12% of all patients are admitted for surgical treatment, 15% are admitted for emergency treatment, and 5% are admitted for both. What is the probability that a patient will be admitted for surgery, emergency, or both?

Accepted Answer

$0.32$

Question 4

Which of the following statements about the $p$-value is correct?

Accepted Answer

A small $p$-value indicates that observing a sample more extreme than the one you obtained is unlikely; therefore, your observed sample is inconsistent with $H_0$.

Question 5

You are constructing a 99% confidence interval for the population mean. Compared to a 95% confidence interval, the 99% confidence interval will:

Accepted Answer

Be wider than the 95% confidence interval.

Question 6

A sample of 100 students has a mean internet usage of 5.02 hours and a standard deviation of 1.377. What is the sample variance?

Accepted Answer

$1.897$

Question 7

A researcher collected two independent random samples to compare the mean daily sales between two stores. If the $p$-value from their test is $0.045$ and the significance level is $0.05$, which conclusion is correct?

Accepted Answer

Reject $H_0$; the two means are significantly different.

Question 8

Which of the following is NOT one of the four 'V's commonly used to characterize Big Data?

Accepted Answer

Validity

Question 9

Suppose the sample mean of a dataset is $\bar{x} = 20$ and the sample standard deviation is $s = 4$. According to Chebyshev's Rule, at least what proportion of data falls within the interval $[12, 28]$?

Accepted Answer

$0.89$

Question 10

A business analyst wants to compare the mean prices of a product at two stores using a two-tailed hypothesis test. Which is the correct null hypothesis?

Accepted Answer

$H_0: \mu_1 = \mu_2$

Question 11

If the sample size increases while the sample standard deviation remains the same, what would happen to the width of the 95% confidence interval?

Accepted Answer

It would become narrower.

Question 12

A company wants to test if the mean monthly sales in two locations are different. The population variances are not equal. Which test should be used?

Accepted Answer

Two-sample $t$-test with unequal variances (Welch's $t$-test)

Question 13

Which of the following statements about sample hypothesis testing is correct?

Accepted Answer

The $p$-value represents the probability of observing data as extreme as the sample, assuming $H_0$ is true.

Question 14

A sample of 5 data points has $\sum_{i=1}^5 x_i = 20$ and $\sum_{i=1}^5 x_i^2 = 90$. What is the sample variance?

Accepted Answer

$2.5$

Question 15

Which of the following is a discrete numerical variable?

Accepted Answer

The number of students entering a classroom during a 10-minute interval.

Question 16

A sample of 200 students has a mean walking time of 25 minutes and a standard deviation of 5 minutes. According to the empirical rule, approximately what percentage of students walk between 20 and 30 minutes?

Accepted Answer

68%

Question 17

Which of the following statements is correct regarding the relationship between confidence level and confidence interval width?

Accepted Answer

Increasing the confidence level increases the width of the confidence interval.

Question 18

A researcher wants to test if the mean price of consumer goods at Store A is higher than at Store B. Which is the correct alternative hypothesis?

Accepted Answer

$H_1: \mu_A > \mu_B$

Question 19

Which of the following is NOT a reason for using a two-sample $t$-test?

Accepted Answer

To compare the means of two related groups.

Statistics for Business: Final Exam Practice Study Guide

Study Guide - Practice Questions

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