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 complaint 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?
Isaias Perez
In a minimum of 125 words, respond to the following:
The appropriate null statement is Ho: p is greater than or equal to 50 pounds and H1: p is less than 50 pounds. For the problem, we have a sample of 20 bags to determine if we will reject the null statement (that the bags are indeed equal to or greater than 50 pounds) or fail to reject the null statement (the bags are indeed not being filled to or less than 50 pounds). Now, we will have to determine the decision rule, or the level of inconsistency with the data that will lead to a rejection of our null hypothesis. The critical value for a 0.05 significance level is 1.7291. Since we are conducting a left tailed test, the critical value is -1.7291. We will use the t-distribution since we have a small number of samples (less than 30) to determine if our calculated t-value falls within the rejection region. The formula is: t=(sample mean – hypothesized mean)/(sample standard deviation/square root of the number of samples). t=-2.23 which does in fact fall within the rejection region. So with a 95% confidence level, we can state that the bags are being under-filled by the machine. The machine should be recalibrated.
Coleen Maciel
In a minimum of 125 words, respond to the following:
Hello Professor and Class-
Issues like this that have been revealed need to be addressed in an appropriate manner as this can be seen in an unethical view. It is vital for any business or organization to address the concerns or issues of the customers that are supporting their business. Addressing issues as such early on can build a good relationship with customers an keep them for future purchases. The null hypothesis Ho would be the weight of a bag of grass seed is > 50 pounds. The alternative hypothesis is H1 which is the weight of a bag of grass seed which is >50 pounds. We can expect that the sample were 20. So we can calculate that the weight is 49.13 pounds. The critical value has been identified as level a= 0.05 In addition, with the standard deviation of 1.743,- 1729. The test statistic would conclude to -2.232.
With the significance levels being 0.05 there is an considerable that the bags were underfilled and the machinery need to be recalibration.
Thanks,
Coleen
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