The breaking strengths of cables produced by a certain manufacturer have a mean,

, of1850

pounds, and a standard deviation of70

pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim,50

newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be1853

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

level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)

Perform aone-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult alist of formulas.)

Thenull hypothesis:H

0

:

Thealternative hypothesis:H

1

:

The type oftest statistic:(Choose one)

Z

t

Chi square

F

The value of the test statistic:

(Round to at least three decimal places.)

Thecritical valueat the0.01

level of significance:

(Round to at least three decimal places.)

Can we support the claim that the mean breaking strength has increased?

Yes

No