Question

Students investigating the packaging of potato chips purchased 6 bags of Lay's Ruffles marked with a net weight of 28.3 grams. They carefully weighted contents of each bag, and recorded the following weights:

29.3

28.2

29.1

28.7

28.9

28.5

a) What are the requirements to produce a confidence interval for this data? In your opinion, are these conditions met?

b) Summarize this data by finding the mean and standard deviation.

c) For a 90% interval, what is the t critical value that you would use?

d) Produce a 90% confidence interval for the mean weight of the Lay's Ruffles bag.

e) Interpret the interval.

f) Does the company's claim on the bag of 28.3 grams seem reasonable based on your confidence level?

Answer 1

a)

Since sample size is small and it is not given that distribution of weight is normal so researcher need to test whether data is normally distributed or not.

Following is the normal probability plot of the data;

Since normality plot shows a straight line pattern so we can assume that data is normally distributed.

(b)

Following table shows the calculations:

	Weight, X	(X-mean)^2
	29.3	0.267289
	28.2	0.339889
	29.1	0.100489
	28.7	0.006889
	28.9	0.013689
	28.5	0.080089
Total	172.7	0.808334

Sample size: n=6

Mean:

Standard deviation:

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(c)

The critical value is: 2.015

d)

The confidence interval is (28.452, 29.114).

e)

We are 90% confident that true population mean weight of the Lay's Ruffles bag lies in the above interval.

f)

No, since 28.3 grams does not lie in the above interval.