A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 19 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of ?¯x¯ = 1268.3 hours and a sample standard deviation of s = 107.7. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1205 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1205 hours. Round all calculated answers to four decimal places.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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A electronics manufacturer has developed a new type of remote control button that is designed to operate longer before failing to work consistently. A random sample of 19 of the new buttons is selected and each is tested in continuous operation until it fails to work consistently. The resulting lifetimes are found to have a sample mean of ?¯x¯ = 1268.3 hours and a sample standard deviation of s = 107.7. Independent tests reveal that the mean lifetime of the best remote control button on the market is 1205 hours. Conduct a hypothesis test to determine if the new button's mean lifetime exceeds 1205 hours. Round all calculated answers to four decimal places.

1. The null hypothesis is Ho : H = 1205. What is the alternate hypothesis?
А. На : и> 1268.3
В. НА : и < 1205
С. НА
:и> 1205
D. HA
1268.3
:
O E. HA : µ 1205
2. Which of the following conditions must be met to perform this hypothesis test? Select all the correct answers.
A. The number of remote control buttons tested must be normally distributed.
B. We must be able to expect that at least 5 buttons will fail to work consistently.
C. The observations must be independent.
D. The lifetime of remote control buttons must be normally distributed.
E. The sample must be large enough so that at least 10 buttons fail and 10 succeed.
3. Calculate the test statistic t
V =
256.18.1
Transcribed Image Text:1. The null hypothesis is Ho : H = 1205. What is the alternate hypothesis? А. На : и> 1268.3 В. НА : и < 1205 С. НА :и> 1205 D. HA 1268.3 : O E. HA : µ 1205 2. Which of the following conditions must be met to perform this hypothesis test? Select all the correct answers. A. The number of remote control buttons tested must be normally distributed. B. We must be able to expect that at least 5 buttons will fail to work consistently. C. The observations must be independent. D. The lifetime of remote control buttons must be normally distributed. E. The sample must be large enough so that at least 10 buttons fail and 10 succeed. 3. Calculate the test statistic t V = 256.18.1
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