Question 1

A business manager wants to test whether the average sales per day at two different stores are significantly different. Which statistical test is most appropriate for this scenario?

Accepted Answer

Two-sample t-test

Question 2

Which of the following formulas correctly represents the calculation of a sample mean $\bar{x}$ for a dataset with $n$ observations $x_1, x_2, ..., x_n$?

Accepted Answer

$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$

Question 3

A company wants to compare the proportion of customers satisfied with their service before and after a new policy. Which hypothesis test should be used?

Accepted Answer

Test for difference in proportions

Question 4

Suppose a researcher wants to test if the mean income in a city is greater than $\$50,000$. Which is the correct null hypothesis $H_0$?

Accepted Answer

$H_0: \mu = 50,000$

Question 5

Which formula is used to calculate the standard deviation $s$ of a sample with $n$ observations?

Accepted Answer

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

Question 6

A marketing analyst wants to determine if there is a relationship between customer age group and product preference. Which statistical test should be used?

Accepted Answer

Chi-square test for independence

Question 7

Which of the following is the correct formula for a confidence interval for a population mean $\mu$ when the population standard deviation $\sigma$ is unknown?

Accepted Answer

$\bar{x} \pm t_{\alpha/2} \frac{s}{\sqrt{n}}$

Question 8

A business wants to test if the variance in delivery times has decreased after implementing a new process. Which test is most appropriate?

Accepted Answer

Test for equality of variances (F-test)

Question 9

Which formula represents the calculation of the test statistic for a hypothesis test of a single mean when the population standard deviation is unknown?

Accepted Answer

$t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$

Question 10

A company wants to compare the mean productivity of three different departments. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Question 11

Which formula is used to calculate the sample proportion $\hat{p}$ from $x$ successes in $n$ trials?

Accepted Answer

$\hat{p} = \frac{x}{n}$

Question 12

A regression analysis yields the equation $y = 2 + 3x$. What is the predicted value of $y$ when $x = 4$?

Accepted Answer

$y = 14$

Question 13

Which formula is used to calculate the $z$-score for a value $x$ in a population with mean $\mu$ and standard deviation $\sigma$?

Accepted Answer

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

Question 14

A business analyst wants to test if the mean time to complete a task is different from 30 minutes. The sample mean is 32 minutes, sample standard deviation is 4 minutes, and sample size is 25. What is the value of the test statistic?

Accepted Answer

$t = \frac{32 - 30}{4 / \sqrt{25}} = 2.5$

Question 15

Which formula is used to calculate the slope $b_1$ in a simple linear regression model?

Accepted Answer

$b_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$

Question 16

A company wants to know if the mean number of products sold per day is different for two stores. The sample means are 50 and 55, both with standard deviation 10 and sample size 25. What is the value of the test statistic for the difference in means?

Accepted Answer

$t = \frac{50 - 55}{\sqrt{\frac{10^2}{25} + \frac{10^2}{25}}} = -2.5$

Question 17

Which formula is used to calculate the expected frequency in a chi-square test for independence for cell $(i, j)$?

Accepted Answer

$E_{ij} = \frac{(	ext{Row Total})_i 	imes (	ext{Column Total})_j}{	ext{Grand Total}}$

Question 18

A business wants to estimate the mean time customers spend in their store. A random sample of 36 customers has a mean of 20 minutes and a standard deviation of 6 minutes. What is the 95% confidence interval for the mean time spent?

Accepted Answer

$20 \pm 1.96 	imes \frac{6}{\sqrt{36}} = 20 \pm 1.96$

Question 19

Which formula is used to calculate the sum of squared errors (SSE) in a regression model?

Accepted Answer

$SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$

Statistics for Business Syllabus and Core Concepts Study Guide

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