1. You work for a soft-drink company in the quality control division. You are interested in the standard deviation of on

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1. You work for a soft-drink company in the quality controldivision. You are interested in the standard deviation of one ofyour production lines as a measure of consistency. The product isintended to have a mean of 12 ounces, and your team would like thestandard deviation to be as low as possible. You gather a randomsample of 17 containers. Estimate the population standard deviationat a 80% level of confidence. 11.89 11.86 11.88 11.94 11.91 11.9912.06 11.89 11.84 11.96 12.16 11.89 12.06 12.07 12.14 11.96 12.06(Data checksum: 203.56) Note: Keep as many decimals as possiblewhile making these calculations. If possible, keep all answersexact by storing answers as variables on your calculator orcomputer.
a) Find the sample standard deviation:
b) Find the lower and upper χ 2 critical values at 80%confidence: Lower: Upper:
c) Report your confidence interval for σ : ( , )
2. Give a 90% confidence interval,for μ1−μ2μ1-μ2 given the following information.
n1=55n1=55, ¯x1=2.12x¯1=2.12, s1=0.75s1=0.75n2=45n2=45, ¯x2=2.12x¯2=2.12, s2=0.56s2=0.56
____±_____ Use Technology Rounded to 2 decimalplaces.
3. You want to obtain a sample to estimate a populationmean. Based on previous evidence, you believe the populationstandard deviation is approximately σ=60.1σ=60.1. You wouldlike to be 99% confident that your estimate is within 0.5 of thetrue population mean. How large of a sample size is required?
Do not round mid-calculation. However, use a critical valueaccurate to three decimal places — this is important for the systemto be able to give hints for incorrect answers.