Question

In: Statistics and Probability

A manufacturer of AAA batteries performs quality control checks to verify that they fall within their...

A manufacturer of AAA batteries performs quality control checks to verify that they fall within their designed specifications. Battery life is normally distributed, and a sample of 15 batteries yields an average battery life of 142 hours and a standard deviation of 4.8 hours when tested. Create a 95% confidence interval for the population standard deviation of battery life.

Solutions

Expert Solution

Solution:

Given:

Sample size = n = 15

Sample standard deviation = s = 4.8

Confidence level = c = 95%

We have to create a 95% confidence interval for the population standard deviation of battery life.

Formula:

where

and are chi-square critical values for right and left tails.

c = 0.95 , then

Area for right tail critical value:

and Area for left tail critical value:   

df = n - 1 = 15 - 1 = 14

Thus we get:

and

Thus we get:

Thus a 95% confidence interval for the population standard deviation of battery life is between 3.51 hours and 7.57 hours.

(Round final answer to specified number of decimal places)


Related Solutions

A manufacturer of AAA batteries wants to estimate the mean life expectancy of the batteries. A...
A manufacturer of AAA batteries wants to estimate the mean life expectancy of the batteries. A sample of 25 such batteries shows that the distribution of life expectancies is roughly normal with a mean of 44.25 hours and a standard deviation of 2.25 hours. Construct a 98% confidence interval for the mean life expectancy of all the AAA batteries made by this manufacturer
Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation...
Lifetimes of AAA batteries are approximately normally distributed. A manufacturer wants to estimate the standard deviation of the lifetime of the AAA batteries it produces. A random sample of 23 AAA batteries produced by this manufacturer lasted a mean of 10.1 hours with a standard deviation of 2.2 hours. Find a 90% confidence interval for the population standard deviation of the lifetimes of AAA batteries produced by the manufacturer. Then complete the table below. Carry your intermediate computations to at...
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer...
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 86 minutes with a mean life of 505 minutes. If the claim is true, in a sample of 120 batteries, what is the probability that the mean battery life would differ from the population mean by greater than 16.6 minutes? Round your answer to four decimal places.
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer...
A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of 8464 with a mean life of 886 minutes. If the claim is true, in a sample of 145 batteries, what is the probability that the mean battery life would be greater than 904.8 minutes? Round your answer to four decimal places.
Can you please explain me this question? Thanks! A manufacturer of AAA batteries wants to estimate...
Can you please explain me this question? Thanks! A manufacturer of AAA batteries wants to estimate the mean life expectancy of the batteries. A sample of 20 such batteries shows that the distribution if life expectancies is roughly normal with a sample mean of 32.5 and a sample standard deviation of 2.75 hours. Construct a 95% confidence interval for the mean life expectancy of AAA batteries made by this manufacturer.
Exercise 31.1. Rope checks. In a certain manufacturing process, an automated quality control computer checks 10...
Exercise 31.1. Rope checks. In a certain manufacturing process, an automated quality control computer checks 10 yards of rope at a time. If no defects are detected in that 10-yard section, that portion of the rope is passed on. However, if there is a defect detected, a person will have to check the rope over more carefully to determine where (measured from the left side in yards) the defect is. If exactly 1 defect is detected in a rope section,...
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​...
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​ Historically, the failure rate for LED light bulbs that the company manufactures is 18​%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts​ (a) through​ (d) below. a. What is the probability that none of the LED light bulbs are​ defective? The probability that none of the LED light bulbs are defective is . 1374. ​(Type an integer or a...
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​Historically,the...
A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures.​Historically,the failure rate for LED light bulbs that the company manufactures is 14 ​%. Suppose a random sample of 10 LED light bulbs is selected. Complete parts​ (a) through​ (d) below. b.What is the probability that exactly one of the LED light bulbs is ​defective? The probability that exactly one of the LED light bulbs is defective is _____ ​(Typean integer or a decimal. Round...
The quality control director for a clothing manufacturer wanted to study the effect of operators and...
The quality control director for a clothing manufacturer wanted to study the effect of operators and machines on the breaking strength (in pounds) of wool serge material. A batch of material was cut into square yard pieces and these were randomly assigned, two each, to all twelve combinations of four operators and three machines chosen specifically for the equipment. The results were as follows: Operator Machine I Machine II Machine III A 110 117 109 114 113 122 B 108...
2. You work in quality control for a manufacturer, and want to see what proportion of...
2. You work in quality control for a manufacturer, and want to see what proportion of your company’s products pass inspection. You take a sample of 80 products, and find that 65 of them pass inspection. a. What is your point estimate for the proportion that pass b. Use your answer from a) to find a 95% CI for ‘p’ (Remember, you are allowed to use the ‘short-cut’ formula here) c. You want your CI to be accurate to ±1.5...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT