Question

Tests made on the breaking strength of 10 pieces of a metal gave the following results: 578, 572, 570, 568, 572, 570, 570, 572, 598 and 584 kg. Test if the mean breaking strength of the wire can be assumed as 577 kg

Answer 1

$H_0: \mu=577$ kg

$H_a: \mu\neq577$ kg

$t=\frac{\overline{x}-\mu}{s\sqrt{n}}$

$\overline{x}=\sum{x_i}/n=575.4$ kg

$s=\sqrt{\frac{\sum (x_i-\overline{x})|^2}{n-1}}=9.24$ kg

$t=\frac{575.4-577}{9.24/\sqrt{10}}=-3.162$

$df=n-1=10-1=9$

critical value for $\alpha=0.05$ :

$t_{crit}=2.262$

Since $|t|>t_{crit}$ , we reject the null hypothesis.

The mean breaking strength of the wire cannot be assumed as 577 kg