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 accept H₀. We do not have argument to keep the claim that the mean breaking strength has increased

Step-by-step explanation:

Normal Distribution

Population Mean   μ₀  = 1850 pounds

Standard Deviation   σ  =  90 pounds

Type of test

Null Hypothesis                         H₀     ⇒    μ  =  μ₀

Alternative Hypothesis            Hₐ      ⇒    μ > μ₀

A one tail test  (right)

n = 21  as    n  < 30  we use t-student table

degree of fredom   20  

t = 2.845

Sample mean   μ = 1893

Then, we compute t statistics

t(s)  =  [ 1893 - 1850 ] / 90/ √n

t(s)  =   43 * 4,583 / 90

t(s)  = 197,069 / 90

t(s)  =  2,190

And we compare t  and  t(s)

t(s)  =  2.190

t =  2.845

Then  t(s)  <  t

We are in the acceptance zone, we accept  H₀

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