Answer these question **Title**: Constructing a 90% Confidence Interval for Population Mean**Introduction**:This exercise involves using statistical distributions to construct a 90% confidence interval for the population mean, based on a given dataset. The decision depends on the known or unknown nature of the population standard deviation (σ) and the size of the sample (n).**Problem Statement**:- Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean.- Justify your choice of distribution.- If neither distribution is suitable, explain why.- Interpret the results.**Scenario Details**:- In a recent season, the population standard deviation of the yards per carry for all running backs was 1.29.- The yards per carry of 25 randomly selected running backs are: ``` 1.6, 5.6, 3.6, 6.8, 3.5, 4.7, 3.4, 4.4, 3.8, 2.2, 2.6, 5.6, 2.5, 4.4, 4.2 ```**Question**:Which distribution should be used to construct the confidence interval?**Options**:A. **Use a normal distribution** because σ is known and the data are normally distributed.B. **Use a t-distribution** because n < 30 and σ is known.C. **Use a normal distribution** because n < 30, the data are normally distributed, and σ is unknown.D. **Use a t-distribution** because n < 30 and σ is unknown.E. **Cannot use the standard normal distribution or the t-distribution** because σ is unknown, n < 30, and the data are not normally distributed.**Decision**:Select the correct option and compute the confidence interval if applicable.**Options for Calculation**:A. The 90% confidence interval is [ _ , _ ] (Round to two decimal places as needed).B. Neither distribution can be used to construct the confidence interval.**Additional Features**:- Buttons for "Help Me Solve This," "View an Example," "Get More Help," "Clear All," and "Check Answer" are present for interactive assistance.**Conclusion**:By correctly identifying and applying the appropriate statistical method, you will understand how

Given Standard deviation = 1.29 n = 25 Alpha = 0.10

Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean. Justify your decision. If neither distributior can be used, explain why. Interpret the results. In a recent season, the population standard deviation of the yards per carry for all running backs was 1.29. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 1.6 5.4 2.7 2.5 6.8 5.3 3.8 4.7 4.4 3.8 2.6 2.2 2.6 5.6 2.5 4.7 5.6 3.6 3.5 5.9 3.9 4.4 4.4 4.6 4.2 Which distribution should be used to construct the confidence interval? ...... A. Use a normal distribution because o is known and the data are normally distributed. O B. Use a t-distribution because n< 30 and o is known. O C. Use a normal distribution because n<30, the data are normally distributed and o is unknown. O D. Use a t-distribution because n< 30 and o is unknown. O E. Cannot use the standard normal distribution or the t-distribution because o is unknown, n< 30, and the data are not normally distributed. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. O A. The 90% confidence interval is ( ). (Round to two decimal places as needed.) O B. Neither distribution can be used to construct the confidence interval.

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...