Question

Managers at an automobile manufacturing plant would like to examine the mean completion time for an assembly line operation. The past data indicate that the mean completion time is 44 minutes, but the managers have reason to believe that this value has decreased. The managers plan to perform a statistical test of the claim and choose a random sample of 125 completion times in preparation for this test. Suppose that the population of completion times for the assembly line operation has a standard deviation of 6 minutes and that the managers perform their hypothesis test using the 0.05 level of significance Based on this information, answer the questions below. Carry your intermediate computations to at least four decimal places, and round your responses as Indicated (If necessary, consult a list of formulas.) What are the nul and alternative hypotheses that the managers should use for the test? is less than less than or equal to greater than greater than or et not equal to equal to Assuming that the actual value of 42.7 minutes, what is tre power of the best Round your response to a least two decimal places. What is the probabilty that the managers reject the hypothesis when, in fact, it is true? Round your response O to at least two decimal places

Answer 1

null hypothesis:Ho μ		greater than or equal to	44
Alternate Hypothesis:Ha μ		less than	44

2)

for 0.05 level with left tail test , critical z=

-1.645

(from excel:normsinv(0.05)

sample size    n=		125
std deviation σ=		6.00
std error ='σx=σ/√n=6/√125=		0.537

rejection region: Xbar <=μ+Zα*σx or Xbar<= 44-1.64485363*0.537=

43.1173

P(Power) =P(Xbar<43.1173|μ=42.7)=P(Z>(43.1173-42.7)/0.537)=P(Z<0.78)=0.78

3)

P(reject the null given it is true) = 0.05

4_)

The probability of committing a Type II error in the second test is greater