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 5.7 millimeters (mm) with a standard deviation of 0.16 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 9 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 5.58 mm

H0:

Ha:

(b) Harry thinks that prices in Caldwell are higher than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $18.35 with standard deviation $2.47. He takes a sample from 4 local Caldwell stores and finds the average price for this same brand of detergent is $17.09.

H0:

Ha: