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 2.5 millimeters (mm) with a standard deviation of 0.17 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 17 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 2.57 mm.

H0:

Ha:

(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 $16.35 with standard deviation $2.20. He takes a sample from 3 local Caldwell stores and finds the average price for this same brand of detergent is $14.40.

H0:

Ha:

If there is no statistical significance in the test then it is know as the null which is denoted by [tex]H_0[/tex], otherwise it is known as alternative hypothesis denoted by [tex]H_a[/tex].

Part (A): The diameter of a spindle in a small motor is supposed to be 2.5 millimeters (mm) if the spindle is either too small or too large, the motor will not work properly.

Thus, the required null and alternative hypothesis are:

[tex]H_0:\mu=2.5[/tex] and [tex]H_a:\mu\neq2.5[/tex]

Part (B) The nationwide average price of a certain brand of laundry detergent is $16.35 and Harry thinks that prices in Caldwell are lower than the rest of the country.

Thus, the required null and alternative hypothesis are:

[tex]H_0:\mu=16.35[/tex] and [tex]H_a:\mu<16.35[/tex]