Question

Please Write this in computer, not by the hand.

10. Answer the following:

There are many products that on their label, establish a content of the packaging. Select a brand of cleaning detergent (for example ACE or Tide).

In their label, they establish a weight of the amount of detergent in each box. Choose a sample of 8 boxes from the selected company and weight the 8 samples on a scale.

Collect this information and build a hypothesis test, a confidence interval, a P – value and size of sample (n) by comparing the average weight of the samples with the one on the box label.

It determines, through the hypothesis test, if there is any difference in the average weight of the sample boxes with the one that appears in the box. Use an alpha for this 0.01 test.

• What is your conclusion?

Answer 1

Weights in grams of a sample of eight 520-gram detergent packs …

Weight (g)
465
537
509
530
456
526
497
489

Hypotheses:

Ho: The mean weight is 520 grams (μ = 520)

Ha: The mean weight is different from 520 grams (μ ≠ 520)

Data:     

n = 8    

μ = 520    

s = 30.02    

x-bar = 501.125    

Hypotheses:    

Ho: μ = 520    

Ha: μ ≠ 520    

Decision Rule:    

α = 0.01    

Degrees of freedom = 8 - 1 = 7

Lower Critical t- score = -3.499483297   

Upper Critical t- score = 3.499483297   

Reject Ho if |t| > 3.499483297   

Test Statistic:    

SE = s/√n = 30.02/√8 = 10.61367279   

t = (x-bar - μ)/SE = (501.125 - 520)/10.6136727856101 = -1.77837

p- value = 0.118577742    

Decision (in terms of the hypotheses):   

Since 1.778366488 < 3.499483 we fail to reject Ho

Conclusion (in terms of the problem):   

There is no sufficient evidence that the mean weight is significantly different from 520 grams.