Question 1

Which of the following best describes the purpose of descriptive statistics in business analytics?

Accepted Answer

To summarize and present data in a meaningful way, such as through graphs and measures of central tendency.

Question 2

A company wants to estimate the average time customers spend on their website. They collect a random sample of 100 customers and find a sample mean of 5.2 minutes with a standard deviation of 1.1 minutes. Which formula should they use to construct a 95% confidence interval for the population mean?

Accepted Answer

$$ \bar{x} \pm t^* \frac{s}{\sqrt{n}} $$

Question 3

Which of the following is NOT a measure of central tendency?

Accepted Answer

Variance

Question 4

A business analyst is using Excel to calculate the probability of exactly 3 successes in 10 independent trials, where the probability of success on each trial is 0.2. Which Excel function should they use?

Accepted Answer

BINOM.DIST

Question 5

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

Accepted Answer

The distribution of sample means will be approximately normal for large sample sizes, regardless of the population distribution.

Question 6

A pharmaceutical company wants to test if a new drug changes the average recovery time from a certain illness. Which type of hypothesis test should they use?

Accepted Answer

A one-sample t-test for the mean

Question 7

If a business wants to compare the average sales between two independent stores, which statistical test is most appropriate?

Accepted Answer

Two-sample t-test

Question 8

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

Accepted Answer

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

Question 9

A marketing manager wants to know if there is a relationship between gender (male/female) and preference for a new product (like/dislike). Which statistical test should be used?

Accepted Answer

Chi-square test for independence

Question 10

A company claims that at least 80% of its deliveries arrive on time. In a random sample of 100 deliveries, 75 were on time. What is the value of the sample proportion $$ \hat{p} $$?

Accepted Answer

$$ \hat{p} = 0.75 $$

Question 11

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis

Question 12

A business analyst uses Excel's NORM.DIST function to find the probability that a value is less than 120, given a mean of 100 and a standard deviation of 15. Which of the following is the correct Excel formula?

Accepted Answer

NORM.DIST(120, 100, 15, TRUE)

Question 13

Which of the following is an example of a categorical variable?

Accepted Answer

The color of cars in a parking lot

Question 14

A hospital administrator wants to estimate the average length of stay for patients. Which Excel function can be used to calculate a 95% confidence interval for the mean, assuming the data is normally distributed?

Accepted Answer

CONFIDENCE.NORM

Question 15

Which of the following is the correct formula for the z-score of a value $$ x  in a $$normal distribution with mean $$ \mu $$ and standard deviation $$ \sigma $$?

Accepted Answer

$$ z = \frac{x - \mu}{\sigma} $$

Question 16

A retail store wants to know if a new layout increases average sales. They collect sales data before and after the change from the same stores. Which test should they use?

Accepted Answer

Paired t-test

Question 17

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

Accepted Answer

If we took many samples, about 95% of the calculated intervals would contain the population mean.

Question 18

A call center manager wants to test if the proportion of customer complaints has decreased after a new policy. Which hypothesis test is most appropriate?

Accepted Answer

One-sample z-test for proportions

Question 19

Which of the following Excel functions would you use to calculate the probability of observing a value greater than a certain number in a normal distribution?

Accepted Answer

1 - NORM.DIST(value, mean, standard_dev, TRUE)

Question 20

A business wants to compare the average customer satisfaction scores across three different store locations. Which statistical method should they use?

Accepted Answer

ANOVA (Analysis of Variance)

Statistics 2103 - Statistical Business Analytics: Syllabus and Study Guide

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