Answer to Question #278550 in Statistics and Probability for zah

Question

Ahmad Fishing Line Inc. produces 10kg test line. 12 randomly selected spools are subjected to tensile-strength tests. The results are as follows:

9.8      10.2    9.8      9.8      9.6      9.1

9.7      9.7      10.1    9.4      10.1    9.7

 

Use the fact that tensile strength is normally distributed to decide whether Ahmad Fishing Line’s 10kg test line is not up to specifications. Perform the required hypothesis test at 5% significance level.

 

Answer 1

$n=12 \\ \bar{x} = \frac{9.8+10.2+...+10.1+9.7}{12}=9.75 \\ s = \sqrt{\frac{(9.8-9.75)^2 + (10.2-9.75)^2 + … +(10.1-9.75)^2 +(9.7-9.75)^2}{12-1}} = 0.31 \\ H_0: \mu = 10 \\ H_1: \mu ≠ 10$

Test-statistic

$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \\ t = \frac{9.75 -10}{0.31 / \sqrt{12}} = -2.79 \\ α = 0.05 \\ d.f.=n-1 = 12-1 =11$

$t_{crit}$ = T.INV.2T(0.05,11)

$t_{crit} = ±2.20098 \\ -2.79 < -2.20098$

We reject H₀.

There is enough evidence to conclude that Ahmad Fishing Line’s 10kg test line is not up to specifications.