A large U.S. barks ( 24 U 22 14 12 13 17 22 15 19 23 13 18 The sample mean 17.1. Generally speaking, a low PE ratie indicates a "value or barpain stock. Suppose a recent cepy of a magazine indicated that the PE ratio ofa certain steck index is . Letbe a randem variable representing the yE ratie of al large US. bank stocks. We anormal distribution ande3.7. De these data indicate that the PE ratie of all US. bank stocks is less than (OWhat is the level of significance State the nul and alternate hypotheses. W you use a let-taled, right-taled, or two tailed test OM , t taled OM 18, H, 18, len-taled
A large U.S. barks ( 24 U 22 14 12 13 17 22 15 19 23 13 18 The sample mean 17.1. Generally speaking, a low PE ratie indicates a "value or barpain stock. Suppose a recent cepy of a magazine indicated that the PE ratio ofa certain steck index is . Letbe a randem variable representing the yE ratie of al large US. bank stocks. We anormal distribution ande3.7. De these data indicate that the PE ratie of all US. bank stocks is less than (OWhat is the level of significance State the nul and alternate hypotheses. W you use a let-taled, right-taled, or two tailed test OM , t taled OM 18, H, 18, len-taled
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![---
### Analyzing the Price to Earnings Ratio (P/E) for Large U.S. Banks
The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (e.g., JP Morgan, Bank of America, and others) produced the following P/E ratios:
\[ \text{Where the ratios are as follows:} \]
\[ 24 \quad 26 \quad 14 \quad 23 \quad 17 \quad 22 \quad 15 \quad 19 \quad 23 \quad 13 \quad 11 \quad 18 \]
The sample mean is \(\bar{x} = 17\). Generally, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is \(\mu = 18\). Let \(x\) be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume \(x\) is normally distributed with \(\sigma = 3.7\). Do these data indicate that the P/E ratio of all large U.S. bank stocks is less than 18? Use \(\alpha = 0.01\).
#### Part I: What is the level of significance?
Identify the null and alternate hypotheses. Will this be a left-tailed, right-tailed, or two-tailed test?
- \(H_0: \mu = 18\); \(H_1: \mu < 18\); left-tailed
- \(H_0: \mu = 18\); \(H_1: \mu > 18\); right-tailed
- \(H_0: \mu = 18\); \(H_1: \mu \neq 18\); two-tailed
#### Part II
**(b) What sampling distribution will you use?** Provide the rationale for your choice:
- The standard normal, since we assume a normal distribution with unknown \(\sigma\).
- The standard normal, since we assume \(x\) has a normal distribution with known \(\sigma\).
- The Student’s \(t\), since \(x\) is assumed known with \(\sigma\).
- The Student’s \(t\), since we assume a normal distribution with known \(\sigma\).
**Calculate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5422827a-7860-4e7c-8a0f-f4498bf171e7%2F1d70ef5d-d8e3-41af-8ba9-16c6efd83554%2Fsy6vq7r_processed.png&w=3840&q=75)
Transcribed Image Text:---
### Analyzing the Price to Earnings Ratio (P/E) for Large U.S. Banks
The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (e.g., JP Morgan, Bank of America, and others) produced the following P/E ratios:
\[ \text{Where the ratios are as follows:} \]
\[ 24 \quad 26 \quad 14 \quad 23 \quad 17 \quad 22 \quad 15 \quad 19 \quad 23 \quad 13 \quad 11 \quad 18 \]
The sample mean is \(\bar{x} = 17\). Generally, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is \(\mu = 18\). Let \(x\) be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume \(x\) is normally distributed with \(\sigma = 3.7\). Do these data indicate that the P/E ratio of all large U.S. bank stocks is less than 18? Use \(\alpha = 0.01\).
#### Part I: What is the level of significance?
Identify the null and alternate hypotheses. Will this be a left-tailed, right-tailed, or two-tailed test?
- \(H_0: \mu = 18\); \(H_1: \mu < 18\); left-tailed
- \(H_0: \mu = 18\); \(H_1: \mu > 18\); right-tailed
- \(H_0: \mu = 18\); \(H_1: \mu \neq 18\); two-tailed
#### Part II
**(b) What sampling distribution will you use?** Provide the rationale for your choice:
- The standard normal, since we assume a normal distribution with unknown \(\sigma\).
- The standard normal, since we assume \(x\) has a normal distribution with known \(\sigma\).
- The Student’s \(t\), since \(x\) is assumed known with \(\sigma\).
- The Student’s \(t\), since we assume a normal distribution with known \(\sigma\).
**Calculate
Expert Solution
Step 1
From the given sample data : n=14 , , ƩX= 239
Now , the sample mean is ,
Also given that σ=3.7 , μ0=18 , α=0.01
Since , the population standard deviation (σ) is known.
Therefore , use normal-distribution.
Our aim is to test the claim that the average P\E rate of all large U.S. bank stocks is less than 18.
Here , we use the one sample mean Z-test.
Step by step
Solved in 3 steps with 1 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman