Post a total of 3 substantive responses over 2 separate days for full participation. This includes your initial post and 2 replies to other students or your faculty member.
Hypothesis testing is used in business to test assumptions and theories. These assumptions are tested against evidence provided by actual, observed data. A statistical hypothesis is a statement about the value of a population parameter that we are interested in. Hypothesis testing is a process followed to arrive at a decision between 2 competing, mutually exclusive, collective exhaustive statements about the parameter’s value.
Consider the following scenario: An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complained alleging that the bags are underfilled. A production manager randomly samples a batch and measures the following weights:
Weight, (lbs)
45.6 49.5
47.7 46.7
47.6 48.8
50.5 48.6
50.2 51.5
46.9 50.2
47.8 49.9
49.3 49.8
53.1 49.3
49.5 50.1
To determine whether the bags are indeed being underfilled by the machinery, the manager must conduct a test of mean with a significance level α = 0.05.
In a minimum of 175 words, respond to the following:
State appropriate null (Ho) and alternative (H1) hypotheses.
What is the critical value if we work with a significant level α = 0.05?
What is the decision rule?
Calculate the test statistic.
Are the bags indeed being underfilled?
Should machinery be recalibrated?
Due Day 7
Reply to at least 2 of your classmates or your faculty member. Be constructive and professional in your responses.
CLASSATE 1:
Based on the data set that was given:
45.6 49.5
47.7 46.7
47.6 48.8
50.5 48.6
50.2 51.5
46.9 50.2
47.8 49.9
49.3 49.8
53.1 49.3
49.5 50.1
We would need these calculations first before we can work on this problem.
Mean = 49.13
Standard
Deviation = 1.7433
Sample Size is n=20
The appropriate null is Ho: u>=50 and the alternative hypotheses is H1:u<50.
What is the critical value if we work with a significant level α = 0.05? 0.05 is -t(0.05,(20-1)) = -1.729133
To answer the question about the decision rule, the decision should be that we reject the null hypothesis due to the critical value of -1.729. Calculate the test statistic: T(observed) <-t(alpha,(n-1))= -2.231851 Based on all the information that was provided, yes, the bags are being under-filled. The test statistic fell under the critical value on the distribution. We also had to reject the null hypotheses. Based on the information that was provided, the machinery should be recalibrated.
CLASSMATE 2:
N=20
Sum=982.6
Sample Mean is 982.6/20=49.13
STEDVA =1.743
Significance level=0.05
Null Hypothesis states that grass seeds packets weight 50lbs
Ho: u=50
Ha: u<50
Population mean is u=50
sample size is /x=49.13
sample deviation is s=1.743
Significance level=0.05
Population is normally distributed. Since the sample sample size is less than 30 and population standard deviation is not given use T statistics.
t=-2.232
excel =t.inv(c6,c7-1) =-1.72913 (left tailed test)
This is less than the significance level. The bags are most likely being underfilled. The machine should be recalibrated.
I noticed this test was done after one customer complained. Perhaps they caught it in the initial mis-calibrated stages and they should also put together a set time for recalibration. This could be done as regular scheduled maintenance. They should also track the efficiency of they machines. Maybe it’s a mechanical defect.
It would be stellar to think tests for compliance were done after one complaint. These days, people complain just to complain. Checking and changes aren’t made till it becomes a dire necessity…usually. These are my thoughts.
