Answer to Question #287390 in Statistics and Probability for Chien Arshatonne

Question

Company XYZ prepares this for jam , which are labelled to have a mass of 500 grams. During the preparation the tins are set to have a mean mass of 550 grams with a standard deviation of 20 grams. One tin is selected from a large batch containing 100 and is found to have a mass of 500 grams. Assuming the masses are normally distributed,test whether the mass of this tin is significantly different from 550 grams at 5% level of significance

Answer 1

The hypothesis to be tested is given as

$H_0:\mu=550$

$H_1:\mu\not=550$

The computed z score is given as follows:

 $\bar {x} = 500, \sigma = 20, \mu = 550$

$$Z = \dfrac{\bar{X}-\mu}{\sigma}=\dfrac{500-550}{20}=-2.5$$

The critical z-value is $Z_{\alpha/2} =1.96$

Since $|z|=2.5>1.96=z_c,$ we reject $H_0$  at 5% level of significance and conclude that the mass of the selected tin is significantly different from 550 grams.