Question

The mean breaking strength of cables supplied by a manufacturer is 1,800 with a standard deviation of 100. By a new technique in the manufacturing process it is claimed that the breaking strength of the cables has increased. In order to test this claim a sample of 50 cables is tested. It is found that the mean breaking strength is 1,850. Can you support the claim at 0.01 level of significance?

Answer 1

Sample size n = 50

Sample mean `bar(x)` = 1850

Sample SD S = 100

Population mean µ = 1800

Null hypothesis H₀: µ = 1850

Level of significance µ = 0.01

Test statistic:

z = `(bar(x) - mu)/(sigma/sqrt("n")) ∼ "N"(0, 1)`

z = `(1850 - 1800)/((100/sqrt(50))` 

= `(50)/(100/(7.0711)`

= `(50 xx 7.0711)/100`

= `353.555/100`

= `7.0711/2`

= 3.5355

∴ z = 3.536

Calculated value |z| = 3.536

Critical value at 1% level of significance is `"Z"_(("a")/2)` = 2.33

Inference:

Since the calculated value is greater than table

i.e. `"Z"_(("a")/2)` at 1% level of significance, the null hypothesis is rejected

Therefore, we conclude that we are rejected.

Therefore, we conclude that we can support the manufacturer's claim at the 0.01 level of significance.