Question 1

Explain the assumptions underlying ANOVA along with their violations.

Accepted Answer

ANOVA requires assumptions that the m groups or factor levels being studied represent populations whose outcome measures:
•are randomly and independently obtained,
•are normally distributed, and
•have equal variances.
If these assumptions are violated, then the level of significance and the power of the test can be affected.If sample sizes are equal, violation of the third assumption does not have serious effects on the statistical conclusions; however, with unequal sample sizes, it can.A nonparametric test may be used when the assumptions underlying ANOVA are violated.

Question 2

Use the data given below to answer the following question(s).
The following extract from a manufacturer's database shows a sample of 10 suppliers, their transportation charges, and the estimated and actual total costs of supplying materials.(Note: Assume a significance level of 0.05 wherever necessary.)
 $$\begin{array} { | c | c | c | c | } 
\hline \text { Supplier } & \begin{array} { c } 
\text { Transportation } \
\text { Charges }
\end{array} & \begin{array} { c } 
\text { Estimated Total } \
\text { Cost }
\end{array} & \text { Actual Total Cost } \
\hline \text { Peter } & 340 & 4,500 & 4,680 \
\hline \text { John } & 560 & 4,500 & 4,790 \
\hline \text { Martin } & 480 & 4,500 & 5,110 \
\hline \text { Philip } & 290 & 4,500 & 4,780 \
\hline \text { Mark } & 370 & 4,500 & 4,810 \
\hline \text { Thomas } & 520 & 4,500 & 4,770 \
\hline \text { Taison } & 350 & 4,500 & 5,250 \
\hline \text { David } & 430 & 4,500 & 4,930 \
\hline \text { Carter } & 510 & 4,500 & 5,010 \
\hline \text { Leonard } & 270 & 4,500 & 4,810 \
\hline
\end{array}$$
-On studying the database, the manufacturer found out that the average difference between the estimated and actual total costs was $426.Based on the sample data, can the manufacturer conclude that the average difference between the estimated and actual total costs is different from zero?

Accepted Answer

If $ \mu D $ denotes the population mean difference between the estimated and actual total costs, then the null and the alternative hypotheses are of the form, H₀:μ D=0 vs.H₁:μD ≠0 The above output from the Excel tool shows the critical values are $ \pm 2.26 $. Since $ t $ Stat $ -6.97 $ is much smaller than the lower critical value $ -2.26 $, the null hypothesis is reiected. It can be concluded that the mean of the differences between the estimated and the actual total costs is statistically significant. The $ p $-value $ 0.0001 $ too is essentially zero verifying this conclusion.

Question 3

Type II error occurs when the test:

Accepted Answer

A) correctly fails to reject an actually true null hypothesis. 
B) incorrectly fails to reject an actually false null hypothesis. 
C) correctly rejects an actually false null hypothesis. 
D) incorrectly rejects an actually true null hypothesis. 
A) correctly fails to reject an actually true null hypothesis. 
B) incorrectly fails to reject an actually false null hypothesis. 
C) correctly rejects an actually false null hypothesis. 
D) incorrectly rejects an actually true null hypothesis. B

Question 4

During a study, individuals were asked to rate a product on a scale of 1-5.From the following data, help the researcher determine whether any significant differences exist in opinions among individuals from different regions.(Note: Assume a significance level of 0.05 wherever necessary.)
 $$\begin{array} { | c | c | c | } 
\hline \text { Quintasia } & \text { Paraland } & \text { Bayundera } \
\hline 3 & 1 & 5 \
\hline 4 & 4 & 1 \
\hline 2 & 2 & 3 \
\hline 5 & 2 & 2 \
\hline 1 & 3 & 2 \
\hline 5 & 5 & 5 \
\hline 3 & 5 & 1 \
\hline & 1 & 4 \
\hline & 4 & \
\hline & 2 & \
\hline
\end{array}$$

Accepted Answer

The null hypothesis for ANOVA is that th

Question 5

For a two-sample hypothesis which tests for differences in population parameters (1)and (2), a two-tailed test seeks evidence that population parameter:

Accepted Answer

A) seeks evidence that population parameter (2)is larger than parameter (1). 
B)  (2)is the same as parameter (1). 
C)  (2)is smaller than parameter (1). 
D)  (1)and (2)do not belong to the same data. 
A) seeks evidence that population parameter (2)is larger than parameter (1). 
B)  (2)is the same as parameter (1). 
C)  (2)is smaller than parameter (1). 
D)  (1)and (2)do not belong to the same data.

Question 6

How do test statistics for two-sample tests vary depending on whether the population standard deviations are known, and if not, whether they are assumed to be equal?

Accepted Answer

Selection of the proper test statistic f

Question 7

Use the data given below to answer the following question(s).
The following extract from a manufacturer's database shows a sample of 10 suppliers, their transportation charges, and the estimated and actual total costs of supplying materials.(Note: Assume a significance level of 0.05 wherever necessary.)
 $$\begin{array} { | c | c | c | c | } 
\hline \text { Supplier } & \begin{array} { c } 
\text { Transportation } \
\text { Charges }
\end{array} & \begin{array} { c } 
\text { Estimated Total } \
\text { Cost }
\end{array} & \text { Actual Total Cost } \
\hline \text { Peter } & 340 & 4,500 & 4,680 \
\hline \text { John } & 560 & 4,500 & 4,790 \
\hline \text { Martin } & 480 & 4,500 & 5,110 \
\hline \text { Philip } & 290 & 4,500 & 4,780 \
\hline \text { Mark } & 370 & 4,500 & 4,810 \
\hline \text { Thomas } & 520 & 4,500 & 4,770 \
\hline \text { Taison } & 350 & 4,500 & 5,250 \
\hline \text { David } & 430 & 4,500 & 4,930 \
\hline \text { Carter } & 510 & 4,500 & 5,010 \
\hline \text { Leonard } & 270 & 4,500 & 4,810 \
\hline
\end{array}$$
-Conduct the appropriate type of one-sample test-statistic to determine whether the average transportation charge is less than $430.

Accepted Answer

The hypotheses take the form: @#LAT-DLM& : populat

Question 8

Which of the following is the initial step in conducting a hypothesis test?

Accepted Answer

A) collecting data and calculating a test statistic 
B) selecting a level of significance 
C) identifying the population parameter of interest 
D) determining a decision rule 
A) collecting data and calculating a test statistic 
B) selecting a level of significance 
C) identifying the population parameter of interest 
D) determining a decision rule

Question 9

Which of the following is true about one-tailed and two-tailed tests?

Accepted Answer

A) For standard normal and t-distributions, which have a mean of zero, lower-tail critical values are negative and upper-tail critical values are positive. 
B) For an upper one-tailed test, if the test statistic is greater than the critical value, the decision would fail to reject the null hypothesis. 
C) For a lower one-tailed test, if the test statistic is less than the critical value, thse decision would be to fail to reject the null hypothesis. 
D) For a two-tailed test, if the test statistic is either greater than the upper critical value or less than the lower critical value, the decision would be to fail to reject the null hypothesis. 
A) For standard normal and t-distributions, which have a mean of zero, lower-tail critical values are negative and upper-tail critical values are positive. 
B) For an upper one-tailed test, if the test statistic is greater than the critical value, the decision would fail to reject the null hypothesis. 
C) For a lower one-tailed test, if the test statistic is less than the critical value, thse decision would be to fail to reject the null hypothesis. 
D) For a two-tailed test, if the test statistic is either greater than the upper critical value or less than the lower critical value, the decision would be to fail to reject the null hypothesis.

Question 10

The average cost for the sample of 5 sales of a product is $\bar{x}$ =$230 and the sample standard deviation is s = $17.50.The hypothesized mean is μ₀= $250.Compute the value of the test statistic.

Accepted Answer

A) -2.56 
B) -4.00 
C) -1.67 
D) -3.87 
A) -2.56 
B) -4.00 
C) -1.67 
D) -3.87

Question 11

Level of significance is the probability of:

Accepted Answer

A) incorrectly rejecting an actually true null hypothesis. 
B) correctly failing to reject an actually true null hypothesis. 
C) incorrectly failing to reject an actually false null hypothesis. 
D) correctly rejecting an actually false null hypothesis. 
A) incorrectly rejecting an actually true null hypothesis. 
B) correctly failing to reject an actually true null hypothesis. 
C) incorrectly failing to reject an actually false null hypothesis. 
D) correctly rejecting an actually false null hypothesis.

Question 12

Robin Inc.feared that the average company loss is running beyond $34,000.It initially conducted a hypothesis test on a sample extracted from its database.The hypothesis was formulated as H₀: average company loss $34,000 vs.H₁: average company loss > $34,000.The test resulted in favor of Robin Inc.'s loss not exceeding $34,000.Detailed study of company accounts later revealed that the average company loss had run up to $37,896.Which of the following errors were made during the hypothesis test?

Accepted Answer

A) Type III error 
B) Type II error 
C) Type I error 
D) Type IV error 
A) Type III error 
B) Type II error 
C) Type I error 
D) Type IV error

Question 13

For a one-tailed test, the critical value:

Accepted Answer

A) divides the sampling distribution into three parts. 
B) is the number of standard errors away from the sample mean. 
C) helps determine if the test statistic falls in the rejection region or not. 
D) fails to reject the null hypothesis if the value exceeds the test statistic. 
A) divides the sampling distribution into three parts. 
B) is the number of standard errors away from the sample mean. 
C) helps determine if the test statistic falls in the rejection region or not. 
D) fails to reject the null hypothesis if the value exceeds the test statistic.

Question 14

In a two-sample test for differences in means, the hypotheses are of the form:

Accepted Answer

A) $\begin{array} { l } H _ { 0 } : \mu 1 - \mu _ { 2 } \{ \geq , \leq , \text { or } = \} 0 \ H _ { 1 } : \mu 1 - \mu 2 \{ \geq , ,,\leq, \text { or }=\} 0 \end{array}$ D) $\begin{array}{l} H_{0}: \mu_{1}-\mu_{2}\{>,<\text {, or }=\} 0 \ H_{1}: \mu_{1}-\mu_{2}\{\leq, \geq \text { or } z\} \end{array}$ A) $\begin{array} { l } H _ { 0 } : \mu 1 - \mu _ { 2 } \{ \geq , \leq , \text { or } = \} 0 \ H _ { 1 } : \mu 1 - \mu 2 \{ \geq , ,,\leq, \text { or }=\} 0 \end{array}$ D) $\begin{array}{l} H_{0}: \mu_{1}-\mu_{2}\{>,<\text {, or }=\} 0 \ H_{1}: \mu_{1}-\mu_{2}\{\leq, \geq \text { or } z\} \end{array}$

Question 15

For a two-sample test, explain the procedure used when it is difficult to justify the assumption that the variances of each population are equal.

Accepted Answer

Only rarely are the population variances

Question 16

Which of the following probabilities gives the confidence coefficient?

Accepted Answer

Question 17

In order to reject the null hypothesis, the F-test statistic must be greater than the ________.

Accepted Answer

A) p-value 
B) variance 
C) df 
D) crit 
A) p-value 
B) variance 
C) df 
D) crit

Question 18

Which of the following is a valid one-sample hypothesis test?

Accepted Answer

A) H₀: population parameter ≠ constant vs.H₁: population parameter = constant B) H₀: population parameter > constant vs.H₁: population parameter ≤ constant C) H₀: population parameter < constant vs.H₁: population parameter ≥ constant D) H₀: population parameter = constant vs.H₁: population parameter ≠ constant A) H₀: population parameter ≠ constant vs.H₁: population parameter = constant B) H₀: population parameter > constant vs.H₁: population parameter ≤ constant C) H₀: population parameter < constant vs.H₁: population parameter ≥ constant D) H₀: population parameter = constant vs.H₁: population parameter ≠ constant

Question 19

Which of the following tests is used to determine if two categorical variables are independent?

Accepted Answer

A) Chi-square test 
B) t-test 
C) z-test 
D) ANOVA 
A) Chi-square test 
B) t-test 
C) z-test 
D) ANOVA

Question 20

For a two-sample test for means with the population variance being known, the Excel procedure used is the Excel z-test.

Accepted Answer

A) True 
 B)False

Explain the assumptions underlying ANOVA along with their violations.

Type II error occurs when the test:

For a two-sample hypothesis which tests for differences in population parameters (1)and (2), a two-tailed test seeks evidence that population parameter:

How do test statistics for two-sample tests vary depending on whether the population standard deviations are known, and if not, whether they are assumed to be equal?

Which of the following is the initial step in conducting a hypothesis test?

Which of the following is true about one-tailed and two-tailed tests?

The average cost for the sample of 5 sales of a product is $\bar{x}$ =$230 and the sample standard deviation is s = $17.50.The hypothesized mean is μ₀= $250.Compute the value of the test statistic.

Level of significance is the probability of:

For a one-tailed test, the critical value:

In a two-sample test for differences in means, the hypotheses are of the form:

For a two-sample test, explain the procedure used when it is difficult to justify the assumption that the variances of each population are equal.

Which of the following probabilities gives the confidence coefficient?

In order to reject the null hypothesis, the F-test statistic must be greater than the ________.

Which of the following is a valid one-sample hypothesis test?

Which of the following tests is used to determine if two categorical variables are independent?

For a two-sample test for means with the population variance being known, the Excel procedure used is the Excel z-test.

Introduction to Business Analytics

Analytics on Spreadsheets

Visualizing and Exploring Data

Descriptive Statistical Measures

Probability Distributions and Data Modeling

Sampling and Estimation

Predictive Modeling and Analysis

Regression Analysis

Forecasting Techniques

Simulation and Risk Analysis

Introduction to Data Mining

Linear Optimization

Applications of Linear Optimization

Integer Optimization

Nonlinear and Non-Smooth Optimization

Optimization Models with Uncertainty

Decision Analysis

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Exam 7: Statistical Inference

Explain the assumptions underlying ANOVA along with their violations.

Type II error occurs when the test:

For a two-sample hypothesis which tests for differences in population parameters (1)and (2), a two-tailed test seeks evidence that population parameter:

How do test statistics for two-sample tests vary depending on whether the population standard deviations are known, and if not, whether they are assumed to be equal?

Which of the following is the initial step in conducting a hypothesis test?

Which of the following is true about one-tailed and two-tailed tests?

The average cost for the sample of 5 sales of a product is xˉ\bar{x}xˉ =$230 and the sample standard deviation is s = $17.50.The hypothesized mean is μ₀= $250.Compute the value of the test statistic.

Level of significance is the probability of:

For a one-tailed test, the critical value:

In a two-sample test for differences in means, the hypotheses are of the form:

For a two-sample test, explain the procedure used when it is difficult to justify the assumption that the variances of each population are equal.

Which of the following probabilities gives the confidence coefficient?

In order to reject the null hypothesis, the F-test statistic must be greater than the ________.

Which of the following is a valid one-sample hypothesis test?

Which of the following tests is used to determine if two categorical variables are independent?

For a two-sample test for means with the population variance being known, the Excel procedure used is the Excel z-test.

Introduction to Business Analytics

Analytics on Spreadsheets

Visualizing and Exploring Data

Descriptive Statistical Measures

Probability Distributions and Data Modeling

Sampling and Estimation

Predictive Modeling and Analysis

Regression Analysis

Forecasting Techniques

Simulation and Risk Analysis

Introduction to Data Mining

Linear Optimization

Applications of Linear Optimization

Integer Optimization

Nonlinear and Non-Smooth Optimization

Optimization Models with Uncertainty

Decision Analysis

Filters

The average cost for the sample of 5 sales of a product is $\bar{x}$ =$230 and the sample standard deviation is s = $17.50.The hypothesized mean is μ₀= $250.Compute the value of the test statistic.