Answer to Question #289717 in Statistics and Probability for Nick

Question

 It has been found from experience that the mean breaking strength of a brand of thread is 500 grams. With a S.D of 40gms. From the supplies, received during the last month, a sample of 16 pieces of thread was tested which showed a mean strength of 450 grams. Can we conclude that the thread supplied is inferior.

Answer 1

$n=16\\\bar x=450\\\sigma=40$

The null and alternative hypothesis are,

$H_0:\mu=500\\vs\\H_1:\mu\lt500$

The test statistic is given as,

$Z={\bar x-\mu\over{\sigma\sqrt{n}}}={450-500\over{40\over\sqrt{16}}}={-50\over10}=-5$

The critical value is,

$Z_{\alpha}=Z_{0.05}=-1.645$

The null hypothesis is rejected if $Z\lt Z_{0.05}$.

Clearly, $Z=-5\lt Z_{0.05}=-1.645$ therefore, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the  thread supplied is inferior at $\alpha=0.05$ level of significance.