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6. The Acme Battery Company has developed a new cell phone battery. On average, the battery...

6. The Acme Battery Company has developed a new cell phone battery. On average, the battery lasts 60 minutes on a single charge. The standard deviation is 4 minutes. Suppose the manufacturing department runs a quality control test. They randomly select 7 batteries. The standard deviation of the selected batteries is 6 minutes.

a.What would be the chi-square statistic represented by this test?

b. What are the degrees of freedom for the chi- square statistic?

c.Suppose they repeated the test with a new random sample of 7 batteries. What is the probability that the standard deviation in the new test would be greater than 6 minutes? (Use the applet)

Math   Statistics-And-Probability   
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Answer #1

a) Sample standard deviation = 6

sample size is 7

population standard deviation = 4

b) The sample size n =7

The degrees of freedom are equal to n-1=7-1=6

c) The chi-square statistic is equal to 13.5

We need to compute . Using the properties of the cumulative distribution function, the corresponding probability is computed as follows:

Therefore, based on the information provided, it is concluded that . The probability value obtained comes from a Chi-Square distribution table.

The probability that the standard deviation in the new test would be greater than 6 minutes = 1-0.9643=0.0357

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