When working properly, the amounts of cement that a filling machine puts into 25

Question

When working properly, the amounts of cement that a filling machine puts into 25-kg bags have a standard deviation () of 1.0 kg. In the next column are the weights recorded for thirty bags selected at random from a day’s production. Test H0: 2 = 1 versus H1: 2 > 1 using the = 0.05 level of significance. Assume that the weights are normally distributed. Calculate the test statistic, p-value, and conclusion

26.18 24.22 24.22 25.300 26.48 24.49 25.18 23.97 25.68 24.54 25.83 26.01 25.14 25.05 25.50 25.44 26.24 25.84 24.49 25.46 26.09 25.01 25.01 25.21 25.12 24.71 26.04 25.67 25.27 25.23 Use the following sums: 2. y, 758.62 and y 19.195.7938

Explanation / Answer

for 0.05 level critical value of chi dist at 29 degree of freedom=17.7084

here S2 =((19195.7938)-(758.62)2/30)/29 =0.4247

hence chi stat =(n-1)s2/2 =29*0.4247/1 =12.317

for above test stat p value =0.002872

as p vlaue is less then 0.05 level we reject null hypothesis

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