Question

You work for a soft-drink company in the quality control division. You are interested in the standard deviation of one of your production lines as a measure of consistency. The product is intended to have a mean of 12 ounces, and your team would like the standard deviation to be as low as possible. You gather a random sample of 17 containers. Estimate the population standard deviation at a 98% level of confidence.

11.83	12.12	12.13	11.96	12.15	11.86
12.02	12.02	11.99	12.08	12	11.97
11.97	11.94	11.98	12.05	11.96

(Data checksum: 204.03)

Note: Keep as many decimals as possible while making these calculations. If possible, keep all answers exact by storing answers as variables on your calculator or computer.

a) Find the sample standard deviation:

b) Find the lower and upper χ2 critical values at 98% confidence:
Lower:    Upper:

c) Report your confidence interval for σσ: (  ,  )

Answer 1

number of observations (n) = 17

a). the necessary calculation table :-

x
11.83	0.029501
12.12	0.013981
12.13	0.016445
11.96	0.001744
12.15	0.021975
11.86	0.020096
12.02	0.000333
12.02	0.000333
11.99	0.000138
12.08	0.006121
12	0.000003
11.97	0.001009
11.97	0.001009
11.94	0.003814
11.98	0.000473
12.05	0.002327
11.96	0.001744
	sum=0.121047

sample standard deviation be:-

b). df = (n-1) = (17-1) = 16

chi square critical value for df=16, at 98% confidence (alpha= 0.02) be:-

	excel function	critical value
	=CHISQ.INV.RT(0.99,16)	5.812212
	=CHISQ.INV.RT(0.01,16)	31.99993

c).the 98% confidence interval for the standard deviation be:-

*** if you have any doubts about the problem please mention it in the comment box... if satisfied please LIKE.