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 4.8 millimeters (mm) with a standard deviation of 0.12 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 52 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.74 mm.
H0 :  
Ha :

(b) Harry thinks that prices in Caldwell, Idaho, are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $16.85 with standard deviation $1.19. He takes a sample from 48 local Caldwell stores and finds the average price for this same brand of detergent is $17.57.
H0 :  
Ha :

Answer 1

(a) The diameter of a spindle in a small motor is supposed to be 4.8 millimeters (mm) with a standard deviation of 0.12 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 52 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.74 mm.

GIVEN:

The manufacturer's claim is that "The diameter of a spindle in a small motor is supposed to be 4.8 millimeters (mm)".

Given the sample of 52 spindles and its average diameter of 4.74 mm, the problem is to to determine whether the mean diameter has moved away from the required measurement.

HYPOTHESIS:

Let be the population mean diameter of spindle in a small motor.

Thus the null and alternate hypothesis is given by,

(That is, the popualtion mean diameter of spindle has not moved away from 4.8 millimeters.)

(That is, the popualtion mean diameter of spindle has moved away from 4.8 millimeters.)

Thus the given problem is "Two sided hypothesis test - One sample z test".

(b) Harry thinks that prices in Caldwell, Idaho, are lower than the rest of the country. He reads that the nationwide average price of a certain brand of laundry detergent is $16.85 with standard deviation $1.19. He takes a sample from 48 local Caldwell stores and finds the average price for this same brand of detergent is $17.57.

GIVEN:

The nationwide average price of a certain brand of laundry detergent is $16.85.

Given the sample of 48 local Caldwell stores and the average price for this same brand of detergent is $17.57, the problem is to to determine whether the mean prices in Caldwell, Idaho, are lower than the rest of the country.

HYPOTHESIS:

Let be the population mean price of a certain brand of laundry detergent in Caldwell.

Thus the null and alternate hypothesis is given by,

$ (That is, the population mean price of a certain brand of laundry detergent in Caldwell is greater than or equal to the mean price in rest of country.)

$ (That is, the population mean price of a certain brand of laundry detergent in Caldwell is lower than the mean price in rest of country.)

Thus the given problem is "Left sided hypothesis test - One sample z test".