Question

In: Statistics and Probability

For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol ?μ ,...

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 millimeters (mm) with a standard deviation of 0.18 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 13 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 3.13 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 $24.25 with standard deviation $2.29. He takes a sample from 3 local Caldwell stores and finds the average price for this same brand of detergent is $25.27.

H0: _______. Ha:________

Solutions

Expert Solution

(a) The diameter of a spindle in a small motor is supposed to be 3 millimeters (mm) with a standard deviation of 0.18 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 13 spindles to determine whether the mean diameter has moved away from the required measurement.

That means we want to test if the actual average diameter is different from the required measurement of 3 mm.

Let be the actual average diameter of the spindle. We want to test if

the hypotheses are

ans:

(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 $24.25 with standard deviation $2.29.

Let be the true average price of a certain brand of laundry detergent in Caldwell.

Harry thinks that prices in Caldwell are lower than the rest of the country, that is Harry thinks that . This means, we want to test if .

The hypotheses are

ans:


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