Question

In: Statistics and Probability

A manufacturer claims that the average mileage of his automobiles is at least 25mpg. In a...

A manufacturer claims that the average mileage of his automobiles is at least 25mpg. In a previous study it was found that the standard deviation of the mileage of his automobiles is 3mpg. For a .05 level of significance, what sample size would be recommended if the researcher wants an 80% chance of detecting that is less than 25 miles per gallon when it is actually 24 (to the next whole number)?

A. 71

B. 95

C. 56

D. 28

Solutions

Expert Solution

Hypothesized mean                =μ o        = 25
true mean                                    =μa                                         = 24
standard deviation                  =σ   = 3
for 0.05 level and right tailed test critival value Zα = 1.6449
for 0.2 level of type II error critival value Zβ = 0.8416
required sample size             =n =(Zα+Zβ)2σ2/(μo-μa)2
= 56.00

option C is corect

orchestra answered 2 years ago
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