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Suppose the average lifetime of a certain type of car battery is known to be 60...

Suppose the average lifetime of a certain type of car battery is known to be 60 months. Consider conducting a two-sided test on it based on a sample of size 25 from a normal distribution with a population standard deviation of 4 months.

a) If the true average lifetime is 62 months and a=0.01, what is the probability of a type II error?

b) What is the required sample size to satisfy and the type II error probability of b(62) = 0.1?

math   Statistics-And-Probability   
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Answer #1

a)

Hypothesized mean true mean standard deviation sample size standard error of mean =0%-a/in for 0.01 level and two tailed test critival value Ζα acceptance region: μ-Za*ox < <-l+Za*ơKZ type ll error-probability of not rejecting 60 62 4 25 0.8000 2.58 62.0640 (62.064-μα)/ox)) 0.08) -0.5319-0 0.5319 57.9360 < β P( (57.936-μα)/ox)) <z- = 5.0800 <Z

b)

Hypothesized mean true mean standard deviation for 0.01 level and two tailed test critival value Ζα/2 for 0.1 level of type Il error required sample sizen 60 62 4 2.58 1.28 critival value zß 60.00

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