Question

A random sample of 10 filled sports drink bottles is taken in one bottling plant, and the mean weight of the bottles is found to be 22 ounces with a variance of 0.09 ounces squared. At another plant, 10 randomly selected bottles have a mean weight of 21 ounces with a variance of 0.04 ounces squared. Assuming the weights in both populations are normally distributed and the population variances are equal, test whether there is difference between the average weights of bottles being filled at the two plants. Use α=0.05.

Answer 1

so, we conclude that there is difference between the average weight of bottles being filled at the two plants.

of 10 filled spot plant. The mean mean A random saudple of 10 filled sports deink bottles is. taken in one bottling ne bottling plant. The mean weight of the bottles is found to be 22 ances with va of 0.09 ounces squared. het ni denore the sample size, as the seu and S. Standard deviation Malo - 22 S, -0.09 At another plant, to laudanly selected bottles have a mean weight of 21 ounces coilte a valiance of 0.04 ounces squared het na deuore the sample sige sample mean , xe the and sa staud aed deviation 12 2 10 2 - 21 Sa 20.04 We assume that the population vaciances are equal. We have to test whether there is a diffecence between the average weight of bottle being filled at the hoo plants. So the null bypothests is Ho: M, M2=0 and alterative respotrests is Hi & Hi-Me to Suice both sample sizes all less than 30 Test stanshe ,t = x, X2 - 0 where S8 = (^,-D + M2-D se mituar a 22-21-0 = (0-000.09) 710-00.C 10.0048511 + + 20.0311 = 32.11 New At 220.05, df 2 M, & ad = 10 + 10- 22 18 t critical value. +2.10 Also p value is less than 0.0001 Casuing Calculator) suce test statistie is greatee than critical value, we reject the melk 10+10-2 z o.00485 hypothesis