Use the standard normal distribution or the 1-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. the results.In a recent season, the population standard deviation of the yards per carry for all running backs was 1.28. The yards per carry of 25 randomly selected running backs are shown below. Assume the Yards per carry are normally distributed. **Constructing a 95% Confidence Interval Using the Standard Normal and t-Distributions**In a recent season, the population standard deviation of the yards per carry for all running backs was 1.28. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed.Data: 4.6, 5.5, 4.3, 5.7, 3.3, 5.3, 5.0, 7.3, 6.7, 2.8, 1.3, 1.8, 5.5, 5.2, 6.7, 7.2, 4.6, 7.4, 3.7, 2.2, 5.7, 6.3, 6.7, 6.2, 3.2---**Question:**Which distribution should be used to construct the confidence interval?- **Options:** - A. Use a t-distribution because n < 30 and σ is known. - B. Use a normal distribution because σ is known and the data are normally distributed. - C. Use a t-distribution because n < 30 and σ is unknown. - D. Use a normal distribution because n < 30, the data are normally distributed 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.**Correct Choice**: - Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. - The correct choice is **B. Use a normal distribution because σ is known and the data are normally distributed.**---**Further Instructions:**- **Part A: The 95% confidence interval is [__, __]. (Round to two decimal places as needed.)- **Part B: Neither distribution can be used to construct the confidence interval.**---By selecting the appropriate distribution, the correct confidence interval can be calculated, using the standard formulae, for accurate statistical inference.

Sample size n =25Population standard deviation =1.28Confidence interval = 95%

the results. Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret In a recent season, the population standard deviation of the yards per carry for all running backs was 1.28. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 4.3 1.6 4.6 5.3 5.5 4.6 5.7 7.4 A. The 95% confidence interval is ( 3.3 7.2 5.6 3.3 (Round to two decimal places as needed.) OB. Neither distribution can be used to construct the confidence interval. 7.3 4.2 6.7 6.7 2.8 7.2 Which distribution should be used to construct the confidence interval? OA. Use a t-distribution because n<30 and a is known. B. Use a normal distribution because o is known and the data are normally distributed. OC. Use a t-distribution because n<30 and a is unknown. OD. Use a normal distribution because n<30, the data are normally distributed and a is unknown. OE. Cannot use the standard normal distribution or the t-distribution because a 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. 1.3 6.2 1.8 5.7 K 5.2 6.3 3.7 D

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Use the standard normal distribution or the 1-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. the results. In a recent season, the population standard deviation of the yards per carry for all running backs was 1.28. The yards per carry of 25 randomly selected running backs are shown below. Assume the Yards per carry are normally distributed.

**Constructing a 95% Confidence Interval Using the Standard Normal and t-Distributions**

In a recent season, the population standard deviation of the yards per carry for all running backs was 1.28. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed.

Data:
4.6, 5.5, 4.3, 5.7, 3.3, 5.3, 5.0, 7.3, 6.7, 2.8, 1.3, 1.8, 5.5, 5.2, 6.7, 7.2, 4.6, 7.4, 3.7, 2.2, 5.7, 6.3, 6.7, 6.2, 3.2

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**Question:**
Which distribution should be used to construct the confidence interval?

- **Options:**
- A. Use a t-distribution because n < 30 and σ is known.
- B. Use a normal distribution because σ is known and the data are normally distributed.
- C. Use a t-distribution because n < 30 and σ is unknown.
- D. Use a normal distribution because n < 30, the data are normally distributed 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.

**Correct Choice**:
- Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.

- The correct choice is **B. Use a normal distribution because σ is known and the data are normally distributed.**

---

**Further Instructions:**

- **Part A: The 95% confidence interval is [__, __].
(Round to two decimal places as needed.)

- **Part B: Neither distribution can be used to construct the confidence interval.**

---

By selecting the appropriate distribution, the correct confidence interval can be calculated, using the standard formulae, for accurate statistical inference.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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