Statistical Techniques in Business and Economics
Statistical Techniques in Business and Economics
16th Edition
ISBN: 9780077639723
Author: Lind
Publisher: Mcgraw-Hill Course Content Delivery
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 12, Problem 1C
To determine

Find whether the sample data indicate that the mean account balance has declined from $1,600.

Perform a hypothesis test to see whether the mean number of transactions per customer is more than 10 per month.

Check whether the mean number of transactions per customer is more than 9 per month.

Find whether there is any difference in the mean checking account balances among the four branches. Also find the pair of branches where these differences occur.

Check whether there is a difference in ATM usage among the four branches.

Find whether there is a difference in ATM usage between the customers who have debit cards and who do not have debit cards.

Find whether there is a difference in ATM usage between the customers who pay interest verses those who do not pay.

Expert Solution & Answer
Check Mark

Explanation of Solution

Hypothesis test for mean checking account balance:

Denote μacc as the mean account balance.

The null and alternative hypotheses are stated below:

H0:μacc=1,600

That is, the mean account balance is $1,600.

H1:μacc<1,600

That is, the mean account balance is less than $1,600.

Step-by-step procedure to obtain the test statistic using Excel MegaStat is as follows:

  • In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests.
  • Choose Mean Vs Hypothesized Value.
  • Choose Data Input.
  • Enter A1:A61 Under Input Range.
  • Enter 1,600 Under Hypothesized mean.
  • Check t-test.
  • Choose less than in alternative.
  • Click OK.

Output obtained using Excel MegaStat is as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  1

From the output, the t-test statistic value is –1.30 and the p-value is 0.0994.

Decision Rule:

If the p-value is less than the level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Conclusion:

Consider that the level of significance is 0.05.

Here, the p-value is 0.0994. Since the p-value is greater than the level of significance, by the rejection rule, fail to reject the null hypothesis at the 0.05 significance level.

Thus, the sample data do not indicate that the mean account balance has declined from $1,600.

Hypothesis test for the mean number of transaction10 per customer per month:

Denote μtrans as the mean transaction per customer.

The null and alternative hypotheses are stated below:

H0:μtrans10

The mean number of transaction per customer is less than or equal to 10 per month.

H1:μtrans>10

The mean number of transaction per customer is more than 10 per month.

Step-by-step procedure to obtain the test statistic using Excel MegaStat is as follows:

  • In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests.
  • Choose Mean Vs Hypothesized Value.
  • Choose Data Input.
  • Enter A1:A61 Under Input Range.
  • Enter 10 Under Hypothesized mean.
  • Check t-test.
  • Choose greater than in alternative.
  • Click OK.

Output obtained using Excel MegaStat is as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  2

From the above output, the t-test statistic value is 0.54 and the p-value is 0.2953.

Conclusion:

Since the p-value is greater than the level of significance, by the rejection rule, fail to reject the null at the 0.05 significance level. Therefore, there is no sufficient evidence to conclude that the mean number of transactions per customer is more than 10 per month.

Hypothesis test for mean number of transaction 9 per customer per month:

The null and alternative hypotheses are stated below:

H0:μtrans9

The mean number of transactions per customer is less than or equal to 9 per month.

H1:μtrans>9

The mean number of transaction per customer is more than 9 per month.

Follow the same procedure mentioned above to obtain the test statistic.

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  3

From the above output, the test statistic value is 2.34 and the p-value is 0.0112.

Conclusion:

Here, the p-value is less than the significance level 0.05. Therefore, the advertising agency can be concluded that the mean number of transactions per customer is more than 9 per month.

Hypothesis test for mean checking account balance among the four branches:

The null and alternative hypotheses are given below:

Null hypothesis:

The mean checking account balance among the four branches is equal.

Alternative hypothesis:

The mean checking account balance among the four branches is different.

Step-by-step procedure to obtain the test statistic using Excel MegaStat is as follows:

  • In EXCEL, Select Add-Ins > Mega Stat > Analysis of Variance.
  • Choose One-Factor ANOVA.
  • In Input Range, select thedata range.
  • In Post-Hoc Analysis, Choose When p < 0.05.
  • Click OK.

Output obtained using Excel MegaStat is as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  4

From the above output, the F-test statistic is 3.82 and the p-value is 0.0147.

Conclusion:

The p-value is less than the significance level 0.05. By the rejection rule, reject the null hypothesis at the 0.05 significance level. Therefore, there is a difference in the mean checking account balances among the four branches.

Post hoc test reveals that the differences occur between the pair of branches. The p-values for branches1–2, branches 2–3, and branches 2–4 are less than the significance level 0.05.

Thus, the branches 1–2, branches 2–3, and branches 2–4 are significantly different in the mean account balance.

Test of hypothesis for ATM usage among the branches:

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in ATM use among the branches.

Alternative hypothesis: There is a difference in ATM use among the branches.

Step-by-step procedure to obtain the test statistic using Excel MegaStat is as follows:

  • In EXCEL, Select Add-Ins > Mega Stat > Analysis of Variance.
  • Choose One-Factor ANOVA.
  • In Input Range, select thedata range.
  • In Post-Hoc Analysis, Choose When p < 0.05.
  • Click OK.

Output obtained using Excel MegaStat is as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  5

From the above output, the F-test statistic is 0.57 and the p-value is 0.6391.

Conclusion:

Here, the p-value is greater than the significance level. By the rejection rule, one fails to reject the null at the 0.05 significance level. Therefore, it can be concluded that there is no difference in ATM use among the four branches.

Hypothesis test for the customers who have debit cards:

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in ATM use between customers who have debit cards and who do not have.

Alternative hypothesis: There is a difference in ATM use by customers who have debit cards and who do not have.

Step-by-step procedure to obtain the test statistic using Excel MegaStat is as follows:

  • In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests.
  • Choose Compare Two Independent Groups.
  • Choose Data Input.
  • In Group 1, enter the column of without debit cards.
  • In Group 2, enter the column of debit cards.
  • Enter 0 Under Hypothesized difference.
  • Check t-test (pooled variance).
  • Choose not equal in alternative.
  • Click OK.

Output obtained is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  6

From the above output, the t-test statistic is 0.11 and the p-value is 0.9142.

Conclusion:

Here, the p-value is greater than the significance level. By the rejection rule, one fails to reject the null at the 0.05 significance level. Therefore, there is no difference in ATM use between the customers who have debit cards and who do not have.

Hypothesis test for the customers who pay interest verses those who do not:

The null and alternative hypotheses are stated below:

Null hypothesis: There is no difference in ATM use between customers who pay interest and who do not.

Alternative hypothesis: There is a difference in ATM use by customers who pay interest and who do not.

Step-by-step procedure to obtain the test statistic using Excel MegaStat is as follows:

  • In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests.
  • Choose Compare Two Independent Groups.
  • Choose Data Input.
  • In Group 1, enter the column of Pay interest.
  • In Group 2, enter the column of don’t pay interest.
  • Enter 0 Under Hypothesized difference.
  • Check t-test (pooled variance).
  • Choose not equal in alternative.
  • Click OK.

Output obtained is represented as follows:

Statistical Techniques in Business and Economics, Chapter 12, Problem 1C , additional homework tip  7

From the above output, the t-test statistic is 0.76 and the p-value is 0.4507.

Conclusion:

Here, the p-value is greater than the significance level. By the rejection rule, one fails to reject the null at the 0.05 significance level. Therefore, there is no difference in ATM use between the customers who pay interest and who do not pay.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
According to an economist from a financial company, the average expenditures on "furniture and household appliances" have been lower for households in the Montreal area than those in the Quebec region. A random sample of 14 households from the Montreal region and 16 households from the Quebec region was taken, providing the following data regarding expenditures in this economic sector. It is assumed that the data from each population are distributed normally. We are interested in knowing if the variances of the populations are equal. a) Perform the appropriate hypothesis test on two variances at a significance level of 1%. Include the following information: i. Hypothesis / Identification of populations ii. Critical F-value(s) iii. Decision rule iv. F-ratio value v. Decision and conclusion b) Based on the results obtained in a), is the hypothesis of equal variances for this socio-economic characteristic measured in these two populations upheld? c) Based on the results obtained in a),…
A major company in the Montreal area, offering a range of engineering services from project preparation to construction execution, and industrial project management, wants to ensure that the individuals who are responsible for project cost estimation and bid preparation demonstrate a certain uniformity in their estimates. The head of civil engineering and municipal services decided to structure an experimental plan to detect if there could be significant differences in project evaluation. Seven projects were selected, each of which had to be evaluated by each of the two estimators, with the order of the projects submitted being random. The obtained estimates are presented in the table below.   a) Complete the table above by calculating: i. The differences (A-B) ii. The sum of the differences iii. The mean of the differences iv. The standard deviation of the differences b) What is the value of the t-statistic? c) What is the critical t-value for this test at a significance level of 1%?…
Compute the relative risk of falling for the two groups (did not stop walking vs. did stop).  State/interpret your result verbally.

Chapter 12 Solutions

Statistical Techniques in Business and Economics

Ch. 12 - Prob. 9ECh. 12 - Prob. 10ECh. 12 - Prob. 3SRCh. 12 - Prob. 11ECh. 12 - The following are six observations collected from...Ch. 12 - Prob. 13ECh. 12 - Prob. 14ECh. 12 - Prob. 4SRCh. 12 - Prob. 15ECh. 12 - For exercises 15 and 16, conduct a test of...Ch. 12 - Prob. 17ECh. 12 - Prob. 18ECh. 12 - Prob. 5SRCh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Prob. 21ECh. 12 - Prob. 22ECh. 12 - Prob. 23CECh. 12 - Prob. 24CECh. 12 - Prob. 25CECh. 12 - Prob. 26CECh. 12 - In an ANOVA table, the MSE is equal to 10. Random...Ch. 12 - Prob. 28CECh. 12 - Prob. 29CECh. 12 - Prob. 30CECh. 12 - Prob. 31CECh. 12 - Prob. 32CECh. 12 - Prob. 33CECh. 12 - Prob. 34CECh. 12 - Prob. 35CECh. 12 - Prob. 36CECh. 12 - Prob. 37CECh. 12 - Prob. 38CECh. 12 - Shanks Inc., a nationwide advertising firm, wants...Ch. 12 - Prob. 40CECh. 12 - Prob. 41CECh. 12 - Prob. 42CECh. 12 - Prob. 43CECh. 12 - Prob. 44CECh. 12 - Prob. 45CECh. 12 - Prob. 46CECh. 12 - Prob. 47CECh. 12 - Prob. 48CECh. 12 - Prob. 49DECh. 12 - Prob. 50DECh. 12 - Prob. 51DECh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 1CCh. 12 - Prob. 2CCh. 12 - Prob. 1.1PTCh. 12 - The likelihood of rejecting a true null hypothesis...Ch. 12 - Prob. 1.3PTCh. 12 - Prob. 1.4PTCh. 12 - Prob. 1.5PTCh. 12 - Prob. 1.6PTCh. 12 - In a two-tailed test, the rejection region is...Ch. 12 - Prob. 1.8PTCh. 12 - Prob. 1.9PTCh. 12 - Prob. 1.10PTCh. 12 - Prob. 2.1PTCh. 12 - Prob. 2.2PTCh. 12 - Prob. 2.3PT
Knowledge Booster
Background pattern image
Statistics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Text book image
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Text book image
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License