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Practice for Hypothesis Testing (with z) 2. Batteries are supposed to last for 13 hours with...

Practice for Hypothesis Testing (with z)

2. Batteries are supposed to last for 13 hours with a standard deviation of 0.31 hours. The quality control engineer is testing a new operating system and finds that a sample of 43 devices using the new operating system exhausts the batteries in a mean of 12.89 hours. Test to determine if the average life of the batteries when using the new operating system is significantly less than the stated life of 13 hours using a= 0.05.

math   Statistics-And-Probability   
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Answer #1

We need to test if average life of the batteries when using the new operating system is significantly less than the stated life of 13 hours so our hypotheses will be:

Ho: \small \mu = 13

H1: \small \mu < 13 [Left Tailed Test]

Test statistic

12.89 – 13 0.31/43

z = -2.327

Critical z value for 0.05 significance level and a left tailed test = -1.65

Since calculated z is less than critical value, we reject the null hypothesis. Hence,

We have sufficient evidence to conclude that the average life of the batteries when using the new operating system is significantly less than the stated life of 13 hours.

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