Question 1

A technology company wants to test whether a new chatbot system reduces average customer chat response time. They collect before-and-after data for 28 customers. Which hypothesis test is most appropriate?

Accepted Answer

A Paired Sample t-Test (Dependent Samples)

Question 2

A retailer tests three different checkout scanners and records the average checkout time for each. Which analytical technique should be used to compare the three scanners?

Accepted Answer

A One-Way ANOVA

Question 3

A logistics team at MetaShip Logistics wants to ensure that their average delivery time is less than 4.0 days. They collect a sample of 20 deliveries and find a sample mean of 4.2 days, with a sample standard deviation of 0.5 days. What are the null and alternative hypotheses for this test?

Accepted Answer

$H_0: \mu \leq 4.0$; $H_a: \mu > 4.0$

Question 4

A fast-casual restaurant introduces a new kitchen layout and wants to test if the average prep time decreased. The sample mean before is 8.0 min, after is 6.8 min, with $n=25$ for each. Which test should be used?

Accepted Answer

Paired Sample t-Test (Matched Pairs)

Question 5

A company tests whether two vendors, Vendor North and Vendor South, have different average chat handle times. The sample means are 3.2 min and 3.6 min, respectively, with similar variances. What is the correct null hypothesis?

Accepted Answer

$H_0: \mu_{North} = \mu_{South}$

Question 6

A national retailer uses four regional suppliers and wants to compare their average delivery times. Which are the correct hypotheses for a one-way ANOVA?

Accepted Answer

$H_0: \mu_1 = \mu_2 = \mu_3 = \mu_4$; $H_a:$ At least one mean differs

Question 7

A beverage company wants to check if the average fill volume of their 600 mL bottles differs from the target. They collect a sample of 40 bottles. Which test is most appropriate?

Accepted Answer

One-Sample t-Test

Question 8

A company pilots three scheduling models to improve customer satisfaction scores (CSAT). The means are: Classic Roster = 3.8, Flex Shifts = 4.0, AI-Assist = 4.2. At $\alpha = 0.05$, the ANOVA F-statistic is significant. What conclusion should be drawn?

Accepted Answer

There are significant differences in average CSAT among the models.

Question 9

A company tests whether a new onboarding program reduces average onboarding time. The sample mean before is 15 days, after is 13 days, with $n=30$ for each. The p-value for the test is 0.023 (one-tailed). At $\alpha = 0.05$, what is the correct decision?

Accepted Answer

Reject $H_0$; there is sufficient evidence the program reduced onboarding time.

Question 10

A supermarket tests new barcode scanners and finds a 95% confidence interval for the mean checkout time difference (new - old) is $(-0.28, 0.08)$ minutes. What does this interval imply?

Accepted Answer

There is no statistically significant difference in checkout time between scanners.

Question 11

A company tests whether Plant Alpha has a shorter average packaging cycle time than Plant Beta. The 95% confidence interval for the mean difference (Alpha - Beta) is $(-4.42, -2.27)$ minutes. What does this interval indicate?

Accepted Answer

Plant Alpha is significantly faster than Plant Beta.

Question 12

A company tests three sales training programs and finds the ANOVA F-statistic is not significant at $\alpha = 0.05$. What is the correct business interpretation?

Accepted Answer

There is no statistically significant difference in average sales increase among the programs.

Question 13

A regression analysis finds that the coefficient for 'Number of Agents' is $-0.25$ with a 95% confidence interval of $(-0.34, -0.16)$. What does this mean?

Accepted Answer

Each additional agent is associated with a decrease in average response time between 0.16 and 0.34 minutes.

Question 14

A company tests whether a new kitchen layout reduces prep time. If they conclude the layout reduced prep time when it actually did not, what type of error is this?

Accepted Answer

Type I Error

Question 15

A company tests whether a process deviates from the specified target. If they conclude the process meets the target when it actually deviates, what error has occurred?

Accepted Answer

Type II Error

Question 16

A regression analysis for warehouse replenishment delay finds the coefficient for 'Warehouse Distance' is $0.04$ with a 95% confidence interval of $(0.01, 0.07)$. What does this mean?

Accepted Answer

Each additional hour of warehouse distance increases replenishment delay by between 0.01 and 0.07 hours.

Question 17

A company pilots three scheduling models and finds the Tukey HSD test shows only Classic Roster and AI-Assist differ significantly. What is the best recommendation?

Accepted Answer

AI-Assist should be prioritized; it produces significantly higher CSAT than Classic Roster.

Question 18

A company tests whether a new onboarding program improves onboarding time. If they conclude onboarding improved when it actually did not, what error has occurred?

Accepted Answer

Type I Error

Statistics for Business: Exam 2 Prep Study Guide

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