The breaking strengths of cables produced by a certain manufacturer have historically had a mean of1900

pounds and a standard deviation of50

pounds. The company believes that, due to an improvement in the manufacturing process, the mean breaking strength,

,of the cables is now greater than1900

pounds. To see if this is the case,27

newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be1926

pounds. Assume that the population is normally distributed. Can we support, at the0.01

level of significance, the claim that the population mean breaking strength of the newly-manufactured cables is greater than1900

pounds? Assume that the population standard deviation has not changed.

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult alist of formulas.)

(a)State the null hypothesisH

0

and the alternative hypothesisH

1

.H

0

:

H

1

:

(b)Determine the type of test statistic to use.

(Choose one)

(c)Find the value of the test statistic. (Round to three or more decimal places.)

(d)Find thep-value. (Round to three or more decimal places.)

(e)Can we support the claim that the population mean breaking strength of the newly-manufactured cables is greater than1900

pounds?YesNo