Question

Establish the appropriate hypotheses for the following situations:

a) A corporation has used a specific manufacturing process for many months in order to manufacture a specific product. The design and manufacturing engineers have developed a new process. Two controlled experiments were performed, one for each method, in order to compare them. The process will only be changed if there is strong evidence that the proportion of defectives us reduced by 5%.

b) You are an engineer in charge of a process in a production line. It is known that the concentration of nitrogen in the mix must be .02 gm/litre in order for the process to give the appropriate results. If the nitrogen concentration is too high or too low, the process will lose control and production must be halted in order to adjust it.

c) You work for a magazine specializing in cars. Your job is to carry out an experiment with two brands of gasoline in order to determine which one has better average performance.

d) The admissions office has been using the scores of an aptitude test designed by the university. The score distribution is a Normal with μ = 2200 and σ = 100. The university proposes the use of a new test named Index of Intelligence and Abilities. The test will only be changed if there is an increase in variability. An experiment was carried out with 400 students by giving them the new test only.

Answer 1

(a) H0: Null Hypothesis: P1 - P2 0.05

HA: Alternative Hypothesis: P1 - P2 > 0.05 (Claim)

EXPLANATION: P1 = Population proportion of defectives in old process. P2 = Population proportion of defectives in new process.

(b) H0: Null Hypothesis: = 0.02

HA: Alternative Hypothesis: 0.02

(c) H0: Null Hypothesis: 1 2

HA: Alternative Hypothesis: 1 < 2

EXPLANATION : If by hypothesis tesing, in case H0 is rejected, Brand 2 will be selected. In case Fail to reject H0, Brand 1 is selected.

(d) H0: Null Hypothesis: 100

HA: Alternative Hypothesis: >100