**Overview**Lazurus Steel Corporation manufactures iron rods intended to be 36 inches long. However, due to variations in the manufacturing process, the exact length of each rod may differ slightly. The lengths of these rods follow a normal distribution around a mean value, with occasional deviations. To ensure quality, the mean length when the machinery operates correctly should be 36 inches, with a standard deviation of 0.035 inch.**Quality Control Process**- Each week, the quality control department obtains a sample of 20 rods to assess their mean length.- The department tests the null hypothesis $ \mu = 36 $ inches against the alternative hypothesis $ \mu \neq 36 $ inches.**Recent Observations**- In a recent test, the sample mean length was 36.015 inches for 20 rods.**Instruction for Analysis**You're tasked with calculating the $ p $-value for this hypothesis test. If the $ p $-value suggests significant deviation from the expected mean (with a significance level $\alpha = 0.01$), the machinery will be halted for adjustments.**Calculation Guidance**- Use the normal distribution table.- Provide the $ p $-value rounded to four decimal places.**Question**Based on your $ p $-value, should the quality control inspector adjust the machine if the threshold for Type I error probability is 0.01?$ p $-value = ____(Note: Ensure you perform the calculations needed to fill in the $ p $-value.) The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.25 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months.Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months.Round your answer to four decimal places.\[ p = \]

Name: **Overview**Lazurus Steel Corporation manufactures iron rods intended
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: **Overview**Lazurus Steel Corporation manufactures iron rods intended to be 36 inches long. However, due to variations in the manufacturing process, the exact length of each rod may differ slightly. The lengths of these rods follow a normal distribu

Note- Since both are different questions, so according to our policy we can answer only one…

Answered: Lazurus Steel Corporation produces iron…

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

Related questions

Concept explainers

Topic Video

Question

**Overview**

Lazurus Steel Corporation manufactures iron rods intended to be 36 inches long. However, due to variations in the manufacturing process, the exact length of each rod may differ slightly. The lengths of these rods follow a normal distribution around a mean value, with occasional deviations. To ensure quality, the mean length when the machinery operates correctly should be 36 inches, with a standard deviation of 0.035 inch.

**Quality Control Process**

- Each week, the quality control department obtains a sample of 20 rods to assess their mean length.
- The department tests the null hypothesis $ \mu = 36 $ inches against the alternative hypothesis $ \mu \neq 36 $ inches.

**Recent Observations**

- In a recent test, the sample mean length was 36.015 inches for 20 rods.

**Instruction for Analysis**

You're tasked with calculating the $ p $-value for this hypothesis test. If the $ p $-value suggests significant deviation from the expected mean (with a significance level $\alpha = 0.01$), the machinery will be halted for adjustments.

**Calculation Guidance**

- Use the normal distribution table.
- Provide the $ p $-value rounded to four decimal places.

**Question**

Based on your $ p $-value, should the quality control inspector adjust the machine if the threshold for Type I error probability is 0.01?

$ p $-value = ____

(Note: Ensure you perform the calculations needed to fill in the $ p $-value.)

$The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.25 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months. Round your answer to four decimal places. \[ p = \]$

Transcribed Image Text:The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.25 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months. Round your answer to four decimal places. \[ p = \]

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Application of Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions