The newest model of a car battery from a popular brand is supposed to have a lifetime of 60 months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of 22 car batteries. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from the random sample. Take Sample Number of carbatteries Sample mean Sample standard deviation Sample variance To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your 99% confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute". Critical values Confidence level Left critical value Right critical value 99% =χ20.9958.034 =χ20.00541.401 95% =χ20.97510.283 =χ20.02535.479 90% =χ20.9511.591 =χ20.0532.671 Point estimate of the population variance: Sample size: Left critical value: Right critical value: Compute 99% confidence interval for the population variance: 99% confidence interval for the population standard deviation: (b)Based on your sample, enter the values for the lower and upper limits to graph the 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. Round the values to two decimal places. 99% confidence interval for the population standard deviation: 0.001.00

The newest model of a car battery from a popular brand is supposed to have a lifetime of 60 months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of 22 car batteries. Follow the steps below to construct a 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.) (a)Click on "Take Sample" to see the results from the random sample. Take Sample Number of carbatteries Sample mean Sample standard deviation Sample variance To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance. Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your 99% confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute". Critical values Confidence level Left critical value Right critical value 99% =χ20.9958.034 =χ20.00541.401 95% =χ20.97510.283 =χ20.02535.479 90% =χ20.9511.591 =χ20.0532.671 Point estimate of the population variance: Sample size: Left critical value: Right critical value: Compute 99% confidence interval for the population variance: 99% confidence interval for the population standard deviation: (b)Based on your sample, enter the values for the lower and upper limits to graph the 99% confidence interval for the population standard deviation of all lifetimes of this model of car battery. Round the values to two decimal places. 99% confidence interval for the population standard deviation: 0.001.00

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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Question

The newest model of a car battery from a popular brand is supposed to have a lifetime of

months, but the lifetime varies slightly from battery to battery. It is known that the population of all lifetimes (in months) of this model of car battery is approximately normally distributed. You are a product reviewer who wants to estimate the standard deviation for this population with a random sample of

car batteries.

Follow the steps below to construct a

99%

confidence interval for the population standard deviation of all lifetimes of this model of car battery. (If necessary, consult a list of formulas.)

(a)Click on "Take Sample" to see the results from the random sample.

Take Sample

Number of car batteries	Sample mean	Sample standard deviation	Sample variance

To find the confidence interval for the population standard deviation, first find the confidence interval for the population variance.

Enter the values of the point estimate of the population variance, the sample size, the left critical value, and the right critical value you need for your

99%

confidence interval for the population variance. (Choose the correct critical values from the table of critical values provided.) When you are done, select "Compute".

Critical values
Confidence level	Left critical value	Right critical value
99%	=χ20.9958.034	=χ20.00541.401
95%	=χ20.97510.283	=χ20.02535.479
90%	=χ20.9511.591	=χ20.0532.671

Point estimate of the population variance:

Sample size:

Left critical value:

Right critical value:

Compute

99%

confidence interval for the population variance:

99%

confidence interval for the population standard deviation:

(b)Based on your sample, enter the values for the lower and upper limits to graph the

99%

confidence interval for the population standard deviation of all lifetimes of this model of car battery. Round the values to two decimal places.

99% confidence interval for the population standard deviation:

0.001.00

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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