Question

5. A company makes fertilizer sold in bags. The company knows the mean weight of fertilizer in their bags is 25lbs. They then install new bag filling machines and want to make sure bags still contain an average of 25lbs of fertilizer. They take a sample of 20 bags from the new machines and find they have the weights shown below. Are the new bag filling machines working correctly? What test did you use? What were the results? How do the results answer the research question?

24.84

25.13

25.18

24.71

25.05

25.37

25.36

24.63

25.27

25.02

25.35

25.42

25.44

24.99

24.62

25.29

24.75

24.90

25.24

24.65

Answer 1

Here we have to test new bag filling machines make sure bags still contain an average of 25lbs of fertilizer.

Null and alternative hypotheses

Ho : = 25

Ha : 25

Level of significance a = 0.05

Test statistic t

t = xbar - / s/√n

t = 25.06 - 25/0.28/√20

t = 0.96

tcritical for a = 0.05 and d.f = n -1 = 19

tcritical = t_{​​​​​​a/2}, n -1  = 2.09

Decision rule : If t > 2.09 we reject the null hypothesis otherwise we fail to reject the null hypothesis

Our t = 0.96 < 2.09

Decision : we fail to reject the null hypothesis.

Conclusion : There is sufficient evidence to conclude the mean weight of fertilizer in their bags is 25lbs