Question

Please write this in computer, not by the hand.

9. Answer the following:

There are many products that on their label, establish a content of the packaging.

Select one product and design an experiment. Construct a hypothesis testing procedure. Select a sample size, and select how you will measure what is specified on the label to determine the sample mean and standard deviation.

Next, according to a level of significance alpha that you select and a level of accuracy determine the sample confidence level and the sample size for that mean.

Answer 1

Weights in grams of a sample of twenty-five 420-gram cake cartons …

Weight (g)
367
370
382
365
442
438
364
387
358
440
408
399
398
365
377
433
396
431
438
352
422
385
440
436
410

Hypotheses:

Ho: The mean weight is 420 grams (μ = 420)

Ha: The mean weight is different from 420 grams (μ ≠ 420)

Data:     

n = 25    

μ = 420   

s = 30.9    

x-bar = 400.12    

Hypotheses:    

Ho: μ = 420   

Ha: μ ≠ 420   

Decision Rule:    

α = 0.05    

Degrees of freedom = 25 - 1 = 24

Lower Critical t- score = -2.063898547   

Upper Critical t- score = 2.063898547   

Reject Ho if |t| > 2.063898547  

Test Statistic:    

SE = s/√n = 30.9/√25 = 6.18   

t = (x-bar - μ)/SE = (400.12 - 420)/6.18 = -3.21683

p- value = 0.003687255   

Decision (in terms of the hypotheses):   

Since 3.216828479 > 2.063899 we reject Ho and accept Ha

Conclusion (in terms of the problem):   

There is sufficient evidence that the mean weight is different from 420 grams.