Question

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol ?μ , e.g.  mu > 1 for the mean is greater than 1,  mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)

(a) The diameter of a spindle in a small motor is supposed to be 3.2 millimeters (mm) with a standard deviation of 0.15 mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 18 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 3.33 mm.
?0 :  
?? :

(b) Harry thinks that prices in Caldwell are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $22.45 with standard deviation $1.04. He takes a sample from 5 local Caldwell stores and finds the average price for this same brand of detergent is $20.27.
?0 :  
?? :

Answer 1

?0 : mu = 3.2
?? : mu not = 3.2

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?0 : mu = 22.45
?? : mu < 22.45