Answer to Question #241097 in Statistics and Probability for darv

Question

A fisherman decides that he needs a line that will weight 5 kilos if he is to catch the size of the fish he desires. He tests 14 pieces of Brand P line and finds a sample mean of 5.6 kilos. If it is known that σ= .4 kilos, what can he conclude about brand P?

Answer 1

$n=14 \\ \bar{x} = 5.6 \\ \sigma = 0.4 \\ H_0 = 5.0 \\ H_1 ≠ 5.0$

Test-statistic:

$Z = \frac{\bar{x} -\mu }{\sigma / \sqrt{14}} \\ Z = \frac{5.6-5.0}{0.4 / \sqrt{14}} = 5.61$

Let use 1 % significance level.

Critical region: Two-tailed test. Reject H₀ if Z ≤ - 2.575 or Z ≥ 2.575.

Since Z= 5.61 exceeds 2.575, reject the null hypothesis at the 1 % significance level.

He can conclude, that a line will NOT weigh 5 kilos.