For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μμ , 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 3.1 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 20 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 2.98 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 $16.25 with standard deviation $2.22. He takes a sample from 4 local Caldwell stores and finds the average price for this same brand of detergent is $14.76. H0 : Ha :
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
For each situation, state the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1. Please do not include units such as "mm" or "$" in your answer.)
(a) The diameter of a spindle in a small motor is supposed to be 3.1 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 20 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 2.98 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 $16.25 with standard deviation $2.22. He takes a sample from 4 local Caldwell stores and finds the average price for this same brand of detergent is $14.76.
H0 :
Ha :
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