A survey of the average amount of cents off that coupons give was conducted by randomly selecting one coupon per page from the coupon sections of a recent edition of *San Jose Mercury News*. The data collected were as follows: 25¢, 75¢, 55¢, 65¢, 30¢, 55¢, 40¢, 65¢, 40¢, 30¢, 55¢, 40¢, 40¢. Assume the underlying distribution is approximately normal.**NOTE:** If using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)### Part (a)1. (i) $\bar{x} =\_\_\_$ ¢ (rounded to two decimal places)2. (ii) $s_x =\_\_\_$ ¢ (rounded to two decimal places)3. (iii) $n =\_\_\_$4. (iv) $n - 1 =\_\_\_$### Part (b)[Section to be filled out]### Part (c)[Section to be filled out]### Part (d)Construct a 95% confidence interval for the population average worth of coupons.1. (i) State the confidence interval. (Round your answers to two decimal places.) - ($\_\_\_$ ¢, $\_\_\_$ ¢) 2. (ii) Sketch the graph.**Diagram Explanation:**- The diagram displays a symmetric bell curve, typical of a normal distribution.- The center of the curve is marked as $\bar{X}$, representing the sample mean.- The confidence level (C.L.) is shown at the center, and the tail areas are labeled as $\alpha/2$, signifying the significance level divided into two equal parts for the confidence interval.3. (iii) Calculate the error bound. (Round your answer to two decimal places.) - $\_\_\_$ ¢

Let x be the average amount of coupons (in cents) The data collected for the average amount of…

Part (b) O Part (c) O Part (d) Construct a 95% confidence interval for the population average worth of coupons. ) State the confidence interval. (Round your answers to two decimal places.) e. (i1) Sketch the graph. C.L. =

Part (b) O Part (c) O Part (d) Construct a 95% confidence interval for the population average worth of coupons. ) State the confidence interval. (Round your answers to two decimal places.) e. (i1) Sketch the graph. C.L. =

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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Concept explainers

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.

Question

A survey of the average amount of cents off that coupons give was conducted by randomly selecting one coupon per page from the coupon sections of a recent edition of *San Jose Mercury News*. The data collected were as follows: 25¢, 75¢, 55¢, 65¢, 30¢, 55¢, 40¢, 65¢, 40¢, 30¢, 55¢, 40¢, 40¢. Assume the underlying distribution is approximately normal.

**NOTE:** If using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

### Part (a)
1. (i) $\bar{x} =\_\_\_$ ¢ (rounded to two decimal places)
2. (ii) $s_x =\_\_\_$ ¢ (rounded to two decimal places)
3. (iii) $n =\_\_\_$
4. (iv) $n - 1 =\_\_\_$

### Part (b)
[Section to be filled out]

### Part (c)
[Section to be filled out]

### Part (d)
Construct a 95% confidence interval for the population average worth of coupons.

1. (i) State the confidence interval. (Round your answers to two decimal places.)
- ($\_\_\_$ ¢, $\_\_\_$ ¢)

2. (ii) Sketch the graph.

**Diagram Explanation:**
- The diagram displays a symmetric bell curve, typical of a normal distribution.
- The center of the curve is marked as $\bar{X}$, representing the sample mean.
- The confidence level (C.L.) is shown at the center, and the tail areas are labeled as $\alpha/2$, signifying the significance level divided into two equal parts for the confidence interval.

3. (iii) Calculate the error bound. (Round your answer to two decimal places.)
- $\_\_\_$ ¢

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