Question

The extrusion length of steel rebar follows a normal distribution with a population standard deviation of 3 inches. There is concern that the settings of for the cut to length encoder has changed from a routing software upgrade. Historically, the length has always been 80 inches. 20 samples were taken at the start of the shift and the average was calculated to be 81”.   Is there sufficient evidence to suggest that the mean cutting length is GREATER than 80 inches? (alpha = 0.05)

State the Null Hypothesis:

State the Alternate:            

State the significance level and one or two tailed:

State the statistic:

State the Decision Rule:

Perform the Calculation – Make the Decision

Interpret the result:

Answer 1

null hypohesis: Ho: <=80

alternate hypothesis:Ha: >80

significance level =0.05 and test is one tailed(right tailed)

as population is normally distributed and population standard deviaiton is know we should use z test statsistic

for 0.05 level and right tailed test ; Decision rule: reject Ho if z >1.645

std error of mean=std deviation/sqrt(n)=3/sqrt(20)=0.671

test statsitic z =(X-mean)/std error=(81-80)/0.671=1.49

as test statistic is not in rejection region we can not reject null hypothesis

we do not have sufciient evidence at 0.05 level to conclude that mean cutting length is GREATER than 80 inches