Answer to Question #287286 in Statistics and Probability for Dommy

Question

Company XYZ prepares this for jam, which are labeled to have a mass of 500grams. During the preparation the tins are set to have mean mass of 550grams with standard deviation 20 grams. One tin is selected from a large batch containing 100 and is mass is 500grams. 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_o : $\mu$ = 550

vs at $\alpha$ = 0.05

H_a : $\mu$ $\not =$ 550

The computed z score is given as follows:

Z_o = $\frac{\bar {X}- \mu}{\delta}$ , where $\bar {x} = 500, \delta = 20, \mu = 550$

= $\frac{500 -550}{20}$

= $-2.5$

The tabulated z value is;

Z$\alpha/2$ = Z_0.05/2 = Z_0.025 = 1.96 or - 1.96

Since the computed z score = - 2.5 is less than tabulated z value = - 1.96, we reject H_o at 5% level of significance and conclude that the mass of the selected tin is significantly different from 550 grams.