An Air Force introductory course in electronics uses a personalized system of instruction whereby each student views a videotaped lecture and then is given a programmed instruction text. The students work independently with the text until they have completed the training and passed a test. Of concern is the varying pace at which the students complete this portion of their training program. Some students are able to cover the programmed instruction text relatively quickly, whereas other students work much longer with the text and require additional time to complete the course. The fast students wait until the slow students complete the introductory course before the entire group proceeds together with other aspects of their training.

A proposed alternative system involves use of computer-assisted instruction. In this method, all students view the same videotaped lecture and then each is assigned to a computer terminal for further instruction. The computer guides the student, working independently, through the self-training portion of the course.

To compare the proposed and current methods of instruction, an entering class of 122 students was assigned randomly to one of the two methods. One group of 61 students used the current programmed-text method and the other group of 61 students used the proposed computer-assisted method. The time in hours was recorded for each student in the study. The following data are provided in the file named *Training*.

We discuss interval estimation and hypothesis testing on the difference between population means in Chapter 10.

- Use appropriate descriptive statistics to summarize the training time data for each method. What similarities or differences do you observe from the sample data?
- Conduct a hypothesis test on the difference between the population means for the two methods. Discuss your findings.
- Compute the standard deviation and variance for each training method. Conduct a hypothesis test about the equality of population variances for the two training methods. Discuss your findings.
- What conclusion can you reach about any differences between the two methods? What is your recommendation? Explain.
- Can you suggest other data or testing that might be desirable before making a final decision on the training program to be used in the future?

Prior to beginning work on this discussion forum, watch the *Week 3 Introduction*__ (Links to an external site.)__ video, and read Chapter 11 in the MindTap ebook by clicking on the **Getting Ready** link for each perspective chapter.

**Step 1: Read:**

**Step 2: Do:**

In a managerial report,

- Use appropriate descriptive statistics to summarize the training time data for each method. What similarities or differences do you observe from the sample data?
- Conduct a hypothesis test on the difference between the population means for the two methods. Clearly state the
**null and alternative hypothesis**and analyze the**p-value**. State your conclusion. - Compute the standard deviation and variance for each training method. Conduct a
**second**hypothesis test about the equality of population variances for the two training methods. Clearly state the**null and alternative hypothesis**and analyze the**p-value**. State your conclusion. - Explain what conclusion you can reach about any differences between the two methods. What is your recommendation? Explain.
- Suggest other data or testing that might be desirable before making a final decision on the training program to be used in the future.

**Step 3: Discuss:**

- What did you find in your analysis of the data? Were there any surprising results? What recommendations would you make based on your findings? Include details from your managerial report to support your recommendations.

**Guided Response:** Review several of your peer’s posts. In a minimum of 100 words each, respond to at least two of your fellow students’ posts in a substantive manner, and provide information that they may have missed or may not have considered regarding the application of Inferences about Population Variances in business and economics. Do you agree with their conclusions? Why or why not?

Post by classmate 1

Hello classmates and Instructor,

I have included the attached data spreadsheet where I ran the F-Test two-Sample for Variances, Descriptive Statistics, and t-Test: Two Sample Assuming Unequal Variances for the case problem – Air Force training Program.

The F-Test two-sample for variance data shows 15.56 variance for the current training program and 6.28 variance for the proposed training program.

The null hypothesis is that the variances of current and proposed methods are the same__,__ they. The alternative hypothesis is that the variances of current and proposed methods will differ.

The rejection rule, using the p-value approach, means we reject h0 if p-value is smaller or equal to alpha = 0.05.

The F-Test Two-Sample for the variances show p-value of 0.0003. Again, considering the rejection rule, the p-value approach, means reject h0 if p value is smaller or equal to alpha = 0.05. The P-value is .0006, with p-value as .05 – h0 is rejected. The population variances are not are equal.

My null hypothesis for the difference in the means scores population and training methods for current and proposed training methods will be equal, while the alternate hypothesis would be that they will differ.

The descriptive statistics show the standard deviation of 3.94, while the proposed standard deviation is 2.51 show the proposed method has less variation meaning student will be more consistent completion time.

The t-Test: Two-Sample Assuming Unequal Variances results show we can determine the methods defer in terms of variance. There is The proposed training method has a smaller variance showing that the completion times are alike, and students are more likely to complete the training in the same amount of time – making the proposed method preferred with the data given.

The F-Test Two-Sample for the variances show p-value of 0.0548. Again, considering the rejection rule, the p-value approach, means reject h0 if p value is smaller or equal to alpha = 0.05. The P-value is .0548, with p-value as .05 – h0 is rejected. The population variances are not equal.

With the data provided, we can conclude that the population does not differ. We also see that the two training programs, current and proposed – are likely to complete the programs more consistently, slightly ahead of the current model.

I would recommend additional considerations/data for this analysis – especially if the purpose is to decide on maintaining the current or a new proposed training program. There are a lot of things to consider, and it would help to know if there was also any other influence, or the purpose of proposing an alternate program.

**Resources**

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., Cochran, J. J., Fry, M. J., & Ohlmann. J. W. (2021). __ Essentials of modern business statistics with Microsoft® Excel® __(8th ed.). Cengage Learning.

Post by classmate 2

**Use appropriate descriptive statistics to summarize the training time data for each method. What similarities or differences do you observe from the sample data?**

The mean from the data shows 75.07 vs 75.43. The difference between this data does not show much of a difference. The variance from the data shows 15.56 vs 6.28. The difference between this data shows a significant difference from the test.

**Conduct a hypothesis test on the difference between the population means for the two methods. Clearly state the null and alternative hypothesis and analyze the p-value. State your conclusion.**

**Null Hypothesis:** There would be equal or no change between the training methods.

**Alternative Hypothesis:** This method would be a faster method.

**Compute the standard deviation and variance for each training method. Conduct a second hypothesis test about the equality of population variances for the two training methods. Clearly state the null and alternative hypothesis and analyze the p-value. State your conclusion.**

For the current method, the standard deviation is 3.94, while the variance is 15.56. For the proposed method, the standard deviation is 2.51, while the variance is 6.28.

**Null Hypothesis:** The variance would have no change.

**Alternative Hypothesis:** Using this method, the variance would be slower.

The **P-Value** is 0.0003. This is less than the significant level which is 0.05. This would result in a rejection of the **Null Hypothesis.**