1.A manufacturer of mountaineering equipment producestraditional​ three-strand climbing rope on two separate production​lines, line 1 and line 2. The manufacturer regularly tests thetensile strength of its ropes by randomly selecting ropes fromproduction and subjecting them to various tests. The results fromthe most recent random sample of ropes are shown below.
Assuming the population of tensile strengths for each line isapproximately normally distributed with equal​ variances, can themanufacturer conclude there is a difference between the meantensile strengths of ropes produced on the two​ lines? Conduct theappropriate hypothesis test at the 0.01 level of significance.
Line 1 Line 2
x overbar x1=7,248 lb x overbar x2=7,725 lb
s1=405 s2=430
n1=25 n2=20
What are the appropriate hypotheses to​ test?
A. H0​: μ1−μ2≥0
HA​: μ1−μ2<0
B. H0​: μ1−μ2≤0
HA​: μ1−μ2>0
C. H0​: μ1−μ2<0
HA​:μ1−μ2≥0
D. H0​:μ1−μ2>0
HA​: μ1−μ2≤0
E. H0​: μ1−μ2≠0
HA​: μ1−μ2=0
F. H0​: μ1−μ2=0
HA​: μ1−μ2≠0
Determine the rejection region for the test statistic t. Selectthe correct choice below and fill in the answer box to choosechoice.
​(Round to four decimal places as​ needed.)
A.
t>?
B.
t
C.
t?
Calculate the value of the test statistic.
t=?(Round to four decimal places as​ needed.)
Since the test statistic ▼ (choose is/ is not )in the rejection​region, ▼(do not reject/reject)the null hypothesis. There is▼(sufficient /insufficient) evidence to conclude that the twopopulation means are different.
