14-56 Doritos Some students checked 6 bags of Doritos marked with a net weight o
ID: 3375923 • Letter: 1
Question
14-56 Doritos Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. a. Do these data satisfy the assumptions for inference? Explain. b. Find the mean and standard deviation of the weights c. Create a 95% confidence interval for the mean weight of such bags of chips. d. Explain in context what your interval means. e. Comment on the company's stated net weight of 28.3 grams f. * Why might finding a bootstrap confidence interval not be a good idea for these data?Explanation / Answer
a) Do these data satisfy the assumptions for inference? Explain
Assumptions for inference: 1) SRS (Simple random sampling) and <10% of the population
Its is specified that the students checked the bags at random And only 6 bags of Doritos are selected so n<6 and is a small sample. So it is less than 10% of the population
Since the conditions are met, we can use the Student’s t model with 5 degrees of freedom for inference on the sample.
b) Find the mean and standard deviation of the observed weights.
Answer : Sample mean = x? = ?X /n
= 173.9/6
=28.9833
Sample standard deviation : s = ?1/(n-1)?(Xi-X)^2
S = ?1(6-1)( 0.648333
S = 0.36009
c) Create a 95% confidence interval for the mean weight of such bags of chips.
formula : ( X - t(?/2)(s/?n) , X + t(?/2)(s/?n) )
= (28.9- (2.517)*(0.36/?6) 28.9+ (2.517)*(0.36/?6) )
= (28.9-0.377 , 28.9+0.377)
= (28.46, 29.41)
d) Explain in context what your interval means
Answer: we are 95% confident that our population mean lies with in the interval(28.46 <µ <29.41 )
e) Comment on the company’s stated net weight of 28.3 grams.
We don’t have enough evidence to support the claim that is the net weight is 28.3 since it is not
Lying with the 95% confidence interval .
So we can conclude that the net weight is not 28.3 grams
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