STATISTICAL ANALYSIS (No long explanation needed. Rate will be given and write the complete solutions.) Choose the correct answer. CI on VarianceDefective alternator and corroded or loose battery charges are a few of the main causes of batterydegradation. A company producing automobile batteries is developing a prototype on their next productand that they claim their batteries will last on average, 3 years with a variance of 1 year. A random sampleof 5 prototype batteries were taken and in the course of the company's product development, havemeasured their lifetimes as 1.9, 2.4, 3.0, 3.5, and 4.2 years.Construct a 95% confidence interval for o' and decide if the company's claim that o = 1 is valid. Assumethe population of battery lives to be approximately normally distributed.O a. 0.29 < o? < 6.74. Because 95% confidence interval for o? is (0.29, 6.74), and 1 is in thatinterval, we can conclude that the company's claim that o? = 1 is validO b. 0.539 < o < 2.596. Because 95% confidence interval for o is (0.539, 2.596), and 1 is in thatinterval, we can conclude that the company's claim that o = 1 is validO. 0.34 < a? < 4.59. Because 95% confidence interval for o? is (0.34, 4.59), and the s² = 0.815is in that interval, we can conclude that the company's claim is validO d. 0.29 < a? < 6.74. 95% confidence interval for o? is (0.29, 6.74)

In order to find the confidence interval for σ2, R software is used.

Answered: STATISTICAL ANALYSIS (No long…

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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A manufacturer of a computer system is interested in improving its customer support services. As a first step its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system failures. Over a period of six months, customers were surveyed and the amount of downtime (in minutes) due to system failures they had experienced during the previous month was collected. The average downtime was found to be 25.09 min and a variance of 144. If it can be assumed that downtime is normally distributed. Obtain a bound above 10% of the downtime of all the customers.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 6.7 ibs/square inch. Assume the variance is known to be 0.64. If the valve was designed to produce a mean pressure of 6.8 ibs/square inch, is there sufficient evidence at the 0.1 level that the valve does not perform to the specifications? State the null and alternative hypothesis for the above scenario.
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 5 lbs/square inch. Assume the variance is known to be 1. If the valve was designed to produce a mean pressure of 5.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.
A carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 61 doors is made, and it is found that they have a mean of 2044 millimeters with a variance of 729. Is there evidence at the 0.05 level that the doors are either too long or too short? State the null and alternative hypotheses for the above scenario.
A research conducted by SSTA022 Class representative at the University of Limpopo indicates that running increases the lifespan among African men. The mean lifespan of 31 African men runners was 34.0% more than the mean lifespan of 31 inactive African men, with variances reported to be 110.25% and 104.04%, respectively. Assuming the populations to be approximately normally distributed with equal variances.i) Can you conclude that there is a significant increase in the lifespan of the men runners over the inactive men at ? = 0.05? ii) Construct a 95% confidence interval for ?1 − ?2.
Suppose a borderline hypertensive is defined as a person whose DBP is between 90 and 95 mm Hg inclusive, and the subjects are 35-44-year-old males whose BP is normally distributed with mean 80 and variance 144. What is the probability that a randomly selected person from this population will be a borderline hypertensive?

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