Jar of peanuts is supposed to have 16 ounces of peanuts. The filling machine ine
ID: 3159082 • Letter: J
Question
Jar of peanuts is supposed to have 16 ounces of peanuts. The filling machine inevitably experiences fluctuations in filling, so a quality-control randomly samples 12 jars of peanuts from the storage facility and measures their contents The data are in the fable Complete parts (d). Click the icon to view the data table (.a) Are the given data normally distributed? Yes No (b) Determine the sample standard deviation The sample standard deviation is or (Round to three decimal place as needed) (c) Construct a 90% confidence interval for tire population standard deviation of the number of ounces of peanuts. The lower bound is oz (Round to three decimal places as needed) The upper bound is oz: (Round to three decimal places as needed) The quality control manager wants the machine to have a population standard deviation below 0.24 ounce Does the confidence interval validate this desire by indicating that the population standard deviation is below 0 24?Explanation / Answer
a)
YES, as there are no outliers. [ANSWER]
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b)
Using technology,
s = sample standard deviation = 0.355779128 [ANSWER]
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c)
As
df = n - 1 = 11
alpha = (1 - confidence level)/2 = 0.05
Then the critical values for chi^2 are
chi^2(alpha/2) = 19.67513757
chi^2(alpha/2) = 4.574813079
Thus, as
lower bound = (n - 1) s^2 / chi^2(alpha/2) = 0.070767824
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) = 0.304354876
Thus, the confidence interval for the variance is
( 0.070767824 , 0.304354876 )
Also, for the standard deviation, getting the square root of the bounds,
( 0.266022224 , 0.551683674 ) [ANSWER]
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d)
NO. The whole interval is above 0.24. [ANSWER]
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