Homework Help is Here – Start Your Trial Now!
Math
Statistics
35 per year. What is the z-value rounded to the nearest hunc evidence to reject the claim? e is -0.54. There is not enough evidence to reject the claim. e is 0.54. There is enough evidence to reject the claim. e is -0.54. There is enough evidence to reject the claim. e is 0.54. There is not enough evidence to reject the claim.

35 per year. What is the z-value rounded to the nearest hunc evidence to reject the claim? e is -0.54. There is not enough evidence to reject the claim. e is 0.54. There is enough evidence to reject the claim. e is -0.54. There is enough evidence to reject the claim. e is 0.54. There is not enough evidence to reject the claim.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
### Understanding Z-Value and Hypothesis Testing: An Example **Context:** An automobile insurance company asserts that its rates for teenage drivers are, on average, $470 less per year compared to another company's rates. To assess this claim, consider the following information: - **Claimed Average Savings:** $470 per year - **Sample Size (n):** 30 customers - **Sample Average Savings:** $435 per year - **Standard Deviation (σ):** $65 per year **Question:** What is the z-value rounded to the nearest hundredth? Is there sufficient evidence to reject the insurance company's claim? **Options:** 1. ○ The z-value is -0.54. There is not enough evidence to reject the claim. 2. ○ The z-value is 0.54. There is enough evidence to reject the claim. 3. ○ The z-value is -0.54. There is enough evidence to reject the claim. 4. ○ The z-value is 0.54. There is not enough evidence to reject the claim. **Explanation:** The z-value is a measure that describes how many standard deviations an element is from the mean. It is calculated using the formula: \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] Where: - \(\bar{x}\) is the sample mean - \(\mu\) is the population mean - \(\sigma\) is the standard deviation - \(n\) is the sample size **Calculation:** Given: - \(\bar{x} = 435\) - \(\mu = 470\) - \(\sigma = 65\) - \(n = 30\) \[ z = \frac{435 - 470}{\frac{65}{\sqrt{30}}} \] \[ z = \frac{-35}{\frac{65}{\sqrt{30}}} \] \[ z = \frac{-35}{11.87} \] \[ z \approx -2.95 \] **Interpreting the Z-Value:** In hypothesis testing, comparing the z-value to critical values from the z-table helps determine the statistical significance. A z-value of -2.95 is quite large in magnitude, indicating that the sample mean is significantly different from the claimed mean at most common significance levels (e.g.,
Transcribed Image Text:### Understanding Z-Value and Hypothesis Testing: An Example **Context:** An automobile insurance company asserts that its rates for teenage drivers are, on average, $470 less per year compared to another company's rates. To assess this claim, consider the following information: - **Claimed Average Savings:** $470 per year - **Sample Size (n):** 30 customers - **Sample Average Savings:** $435 per year - **Standard Deviation (σ):** $65 per year **Question:** What is the z-value rounded to the nearest hundredth? Is there sufficient evidence to reject the insurance company's claim? **Options:** 1. ○ The z-value is -0.54. There is not enough evidence to reject the claim. 2. ○ The z-value is 0.54. There is enough evidence to reject the claim. 3. ○ The z-value is -0.54. There is enough evidence to reject the claim. 4. ○ The z-value is 0.54. There is not enough evidence to reject the claim. **Explanation:** The z-value is a measure that describes how many standard deviations an element is from the mean. It is calculated using the formula: \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] Where: - \(\bar{x}\) is the sample mean - \(\mu\) is the population mean - \(\sigma\) is the standard deviation - \(n\) is the sample size **Calculation:** Given: - \(\bar{x} = 435\) - \(\mu = 470\) - \(\sigma = 65\) - \(n = 30\) \[ z = \frac{435 - 470}{\frac{65}{\sqrt{30}}} \] \[ z = \frac{-35}{\frac{65}{\sqrt{30}}} \] \[ z = \frac{-35}{11.87} \] \[ z \approx -2.95 \] **Interpreting the Z-Value:** In hypothesis testing, comparing the z-value to critical values from the z-table helps determine the statistical significance. A z-value of -2.95 is quite large in magnitude, indicating that the sample mean is significantly different from the claimed mean at most common significance levels (e.g.,
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS