Question

A manufacturer of mountaineering equipment produces traditional three-strand climbing rope on two separate production lines, line 1 and line 2. The manufacturer regularly tests the tensile strength of its ropes by randomly selecting ropes from production and subjecting them to various tests. The results from the most recent random sample of ropes are shown below. Assuming the population of tensile strengths for each line is approximately normally distributed with equal Line 1 Line 2 variances, can the manufacturer conclude there is a difference between the mean tensile strengths of ropes produced on the two lines? Conduct the appropriate hypothesis test at the 0.10 level of significance. X = 7,157 lb X = 6,705 lb S, = 420 S2 = 405 n, = 15 ng = 30 What are the appropriate hypotheses to test? O A. Ho-H, - H220 HAH-H20 OD. HoH-4250 HAH-H2> 0 OB. HO - H2 = 0 HAH-H270 O E. HOH-H20 HAH, -H220 0 C, H, H, --- > 0 HAL-H250 OF. Ho-H, -1270 HAH-H2 = 0

Answer 1

The statistical software output for this problem is:

Two sample T summary hypothesis test: Vi : Mean of Population 1 P2 : Mean of Population 2 -1 - V2 : Difference between two means Ho: P1 - 12 = 0 HA: 1 - 20 (with pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat P-value Pi - 2 452 129.63567 43 3.4866947 0.0011

Hence,

Hypotheses: Option B is correct.

Rejection region: t < -1.6811 or t > 1.6811

Test statistic = 3.4867