Question

Descent, Inc., produces a variety of climbing and mountaineering equipment. One of its products is a traditional three-strand climbing rope. An important characteristic of any climbing rope is its tensile strength. Descent produces the three-strand rope on two separate production lines: one in Bozeman and the other in Challis. The Bozeman line has recently installed new production equipment. Descent regularly tests the tensile strength of its ropes by randomly selecting them to various tests. The most recent random sample of ropes, taken after the new equipment was installed at the Bozeman plant, revealed the following:
Bozeman; x1= 7,200 lbs
S1=425 n1=25,
Challis;x2=7,087
lbs, S2=415, n2=20

Required:
Conduct the appropriate hypothesis test at the 0.10 level of significance.

Answer 1

Solution :

Assuming $\sigma_1^2=\sigma_2^2$

We have to test

$H_0:\mu_1=\mu_2$

Against $H_a: \mu_1 \neq \mu_2$

Level of significance, $\alpha = 0.05$

$s_p=\sqrt{\frac{(n_1-1)s_1^2+ (n_2-1)s_2^2}{n_1+n_2-2}}$

$s_p=\sqrt{\frac{(25-1)(425)^2+ (20-1)(415)^2}{25+20-2}}$

   = 420.6107

Under $H_0$, the t-statistics is as follows:

$t=\frac{(\overline{x_1} - \overline{x_2})}{s_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \sim$             $\text{t with }(n_1+n_2-2) \ DF$

$t=\frac{(7200-7087)}{(420.6107)\sqrt{\frac{1}{25}+\frac{1}{20}}}$

 = 0.90

DF = (25 + 20 - 2)

    = 43

P-value of the test = 0.375

Since the p value is more than 0.05, we fail to reject our null hypothesis.

There is no difference between then mean tensile strength of the ropes that is produced in the Bozeman and Challis.