Question

Company XYZ prepares this for jam, which are labeled 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 gram at 5% level of significance.

Answer 1

The hypotheses to be tested are,

$H_0:\mu=550\\ vs\\ H_1:\mu\not=550$

$x=500,\sigma=20,\alpha=0.05$

The test statistic is given as,

$Z={x-\mu\over\sigma}\\ Z={500-550\over20}={-50\over20}=-2.5$

$Z$ is compared with the standard normal table value at $\alpha=0.05$

The table value is given as,

$Z_{\alpha\over2}=Z_{0.05\over2}=Z_{0.025}=-1.96$

The null hypothesis is rejected if $Z\lt Z_{0.025}$

Since $Z=-2.5\lt Z_{0.025}=-1.96$, we reject the null hypothesis and conclude that there is sufficient evidence to show that the mass of the selected tin is significantly

different from 550 grams at 5% level of significance.