Answered: A new brand ofbattery for use in…

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

$A new brand of battery for use in calculators and cameras is said to last significantly longer than another brand. A camera manufacturer is to test this brand ($ Y $) with brand ($ X $) to see if brand $ Y $ has a longer life. If brand $ Y $ does last longer, the camera manufacturer will equip their new cameras with them. If not, they will equip them with brand $ X $ that is less costly. Twenty cameras are equipped as follows: ten with brand $ Y $ batteries and ten with brand $ X $ batteries and the life of the batteries is measured. Is brand $ Y $ superior (does it last longer) to brand $ X $? To answer this question, the camera manufacturer uses a 0.01 significance level and knows that the populations are normally distributed with equal variances. Sample data are: | Brand X | Brand Y | |-----------------------|-----------------------| | $ n_1 = 10 $ | $ n_2 = 10 $ | | $ \bar{X}_1 = 500 \text{ hours} $ | $ \bar{X}_2 = 650 \text{ hours} $ | | $ s_1^2 = 400 $ | $ s_2^2 = 484 $ | a. State the null and alternative hypotheses. - $ H_0: $ ____________________ - $ H_1: $ ____________________ b. What is the test statistic? - Appropriate test: ____________________ - Test statistic = ____________________ c. What is the decision rule? d. State the conclusion.$

Transcribed Image Text:A new brand of battery for use in calculators and cameras is said to last significantly longer than another brand. A camera manufacturer is to test this brand ($ Y $) with brand ($ X $) to see if brand $ Y $ has a longer life. If brand $ Y $ does last longer, the camera manufacturer will equip their new cameras with them. If not, they will equip them with brand $ X $ that is less costly. Twenty cameras are equipped as follows: ten with brand $ Y $ batteries and ten with brand $ X $ batteries and the life of the batteries is measured. Is brand $ Y $ superior (does it last longer) to brand $ X $? To answer this question, the camera manufacturer uses a 0.01 significance level and knows that the populations are normally distributed with equal variances. Sample data are: | Brand X | Brand Y | |-----------------------|-----------------------| | $ n_1 = 10 $ | $ n_2 = 10 $ | | $ \bar{X}_1 = 500 \text{ hours} $ | $ \bar{X}_2 = 650 \text{ hours} $ | | $ s_1^2 = 400 $ | $ s_2^2 = 484 $ | a. State the null and alternative hypotheses. - $ H_0: $ ____________________ - $ H_1: $ ____________________ b. What is the test statistic? - Appropriate test: ____________________ - Test statistic = ____________________ c. What is the decision rule? d. State the conclusion.

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