Question

Question # 7. Two machines are filling packages. Fifty samples from the first machine find a sample mean of 4.53 kilograms, and ninety samples from the second machine have a sample mean of 4.01 kilograms. The population standard deviation of the first machine is 0.80 kilograms, and the population standard deviation of the second machine is 0.60 kilograms. Test the claim that the machines are filling packages equally.

Answer 1

The null and alternatiev hypothesis is ,

Ho: M1 = 42

$H_a:\mu_1\neq\mu_2$

The test is two-tailed test.

Since , the population standard deviation is known.

Therefore , use normal distribution.

Let , assume that , the significance level=

g= 0,05

The critical values are , $Z_{\alpha/2}=Z_{0.05/2}=\pm 1.96$

The rejection rule is ,

Reject Ho , if Z-stat>1.96 or Z-stat<-1.96

The test statistic is ,

$Z_{stat}=\frac{\bar{X_1}-\bar{X_2}}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}=\frac{4.53-4.01}{\sqrt{\frac{0.80^2}{50}+\frac{0.60^2}{90}}}=4.01$

Decision : Here , Z-stat=4.01>1.96

Therefore , reject Ho.

Conclusion : Hence , there is not sufficient evidence to support the claim that the machines are filling packages equally.