For each situation, state the null and alternative hypotheses: (Type \"mu\" for

Question

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

(a) The manufacturer claims the diameter of a spindle in a small motor is supposed to be 4.1 millimeters (mm) with a standard deviation of 0.14 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 4.21 mm.
H0H0 :  
HaHa :

(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 $18.65 with standard deviation $2.20. He takes a sample from 4 local Caldwell stores and finds the average price for this same brand of detergent is $17.39.
H0H0 :  
HaHa :

Explanation / Answer

Solution :

     We have to state the null and alternative hypotheses:

Instructions : (Type "mu" for the symbol , 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,mu >= 1 for the mean is greater than or equal to 1. Please do not include units such as "mm" or "$" in your answer.)

Part a) The manufacturer claims the diameter of a spindle in a small motor is supposed to be 4.1 millimeters (mm) with a standard deviation of 0.14 mm.

The manufacturer measures the diameter in a sample of 18 spindles to determine whether the mean diameter has moved away from the required measurement. That is we have to test : if the mean diameter is below 4.1 mm or above 4.1 mm.

Thus the claim asked in question is non directional and hence it is two tailed test. Thus we use not = for Ha.

H0 : mu = 4.1

Ha: mu not = 4.1

Part b) Harry thinks that prices in Caldwell are higher than the rest of the country.

Thus claim is : The prices in Caldwell are higher than the rest of the country.

This is directional and towards right side of the mean. Thus this is right tailed test.

He reads that the nationwide average price of a certain brand of laundry detergent is $18.65 with standard deviation $2.20.

Thus

H0 : mu = 18.65   

Ha : mu >> 18.65

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