Week 4 dis | Business & Finance homework help
If we work with a significant level α = 0.05, then the critical value would be -1.645. The decision rule then follows: if our test statistic falls below this value, reject Ho and accept H1; otherwise do not reject Ho.
In order to calculate our test statistic, first find the sample mean which in this case gives us an average bag weight of 49.3lbs (calculated by summing up every pair of weights and dividing it by 10). Next calculate standard error using formula SE = S/sqrt(n), where n is equal to 10 since it is a sample size of 10 pairs; giving us an answer of 0.739lb for standard error after plugging in sample std dev as 1.582lbs into equation given above). Finally use t-test formula t=x–μ/SE ,where x=49.3 and μ=50,t-stats comes out as -2.61 .
Based on these calculations it can be concluded that indeed there are underfilled bags present as our obtained t-stats lies way beyond critical value hence rejecting Null Hypothesis as opposed Alternative which was That Average Weight Bags Produced Less Than 50 Pounds accepted mechanical recalibration therefore recommended ensure accuracy desired packaging results.