Because of high production-changeover time and costs, a director of manufacturing must convince management that a proposed manufacturing method reduces costs before the new method can be implemented. The current production method operates with a mean cost of $220 per hour. A research study will measure the cost of the new method over a sample production period.

a. Develop the null and alternative hypotheses most appropriate for this study.
b. Comment on the conclusion when H0 cannot be rejected.
c. Comment on the conclusion when H0 can be rejected

A. For the situation presented, we find that the researcher assumes that the test with the new method will obtain results at a cost of less than $ 220.

the null hypothesis will be that the operation of the new method will cost not less than $ 220.

the alternative hypothesis will be that the operation of the new method will be less than $ 220

B. With the situation of the exercise we can affirm that the null hypothesis is not rejected, since the director has verified that the cost of the new method is below $ 220, so the new method can be implemented.

C. For this situation, it is observed that the null hypothesis has been rejected, so after verification, the manager has observed that the cost of the new method is less than $ 220, so the manager's proposal can be developed.

a) H0: μ ≥ 220

Ha: μ < 220

b) there is no sufficient evidence to support the claim that the new production method reduces cost

c) there is sufficient evidence to support the claim that the new production method reduces cost

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For the case above;

The null hypothesis is that the mean cost of production is equal or greater than $220 per hour.

H0: μ ≥ 220

The alternative hypothesis is that the mean cost of production is less than $220 per hour

Ha: μ < 220

b) the conclusion when H0 cannot be rejected is that there is no enough evidence to reject the Null hypothesis. So, there is no sufficient evidence to support the claim that the new production method reduces cost

c) the conclusion when H0 can be rejected is that there is enough evidence to reject the Null hypothesis. So, there is sufficient evidence to support the claim that the new production method reduces cost

just sum

10 + 10 = 20

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt