Question

1. The strength limit of a specific type of a cable is random variable with mean value of 1500 kg and standard deviation 175 kg. The factory that manufactures this type of cables claims that they improved the materials that they used and the new resistance limit of the cable has increased. We randomly chose a sample of 50 cables and the mean strength limit was 1570 kg. If the strength limit in the specific type of cable is normally distributed with a significance level of 0.05, can we state that the claim of the manufacture factory is true? Justify your answer.

Answer 1

n=50, =0.05, =175, = 1500, = 1570

Ho : = 1500

Ha : > 1500

formula for test statistics is

z= 2.828

test statistics =2.828

now calculate P-Value

P-value = 1 - P(z < 2.828)

P(z < 2.83)= 0.9977

P-value = 1 - 0.9977

P-value = 0.0023

Rule for decision is

Reject Ho if (P-Value) ( )

here  (P-Value = 0.0023) ( = 0.05)

Hence,

Reject the null hypothesis(Ho).

Therefore there is enough evidence to support the claim that the  resistance limit of the cable has increased.