The breaking strengths of cables produced by a certain manufacturer have a mean µ, of 1850 pounds, and a standard deviation of 90 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 21 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1893 pounds. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed). Carry your intermediate computations to at least three decimal places.

We reject H₀. At 0,05 level of significance we accept the claimed the average breaking strength has increased

Step-by-step explanation:

Normal Distribution

Population Mean     μ₀  = 1850 pounds

Standard Deviation   σ = 90 pounds

Sample mean   μ  = 1893 pounds

n  = 21

degree of fredom 20

Hypothesis test One tail test (right)

Test

Null Hypothesis                H₀     ⇒           μ   =   μ₀  

Alternative Hypothesis    Hₐ     ⇒            μ  >    μ₀  

At 0,05 level of significance and 20 degrees of fredom we look in t-student table to find  value of t

t = 1.7247

Now we compute t statistics

t(s) = (  μ  -  μ₀ ) / σ /√n

t(s) =( 1893 - 1850)/ 90/√21

t(s) = 43* 4,583/90

t(s) = 2,190

Now we need to compare t(s) and t

t(s) > t      2,190 > 1.7247

Then t(s) is out of the acceptance region and we reject H₀