Question

Consider a vending machine that is supposed to dispense eight ounces of soft drink. A random...

Consider a vending machine that is supposed to dispense eight ounces of soft drink. A random sample of 20 cups taken over a one-week period had an average of 7.845 ounces, and a standard deviation of 0.1986. Estimate a 95% confidence interval of the true mean dispensed by the machine and interpret (in a sentence) what it means.

Math   Statistics-And-Probability   
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Answer #1

Given Data

Sample Size = n = 20

Degree of Freedom = n-1 = 20-1 = 19

Sample Mean = x = 7.845

Sample Standard Deviation = s = 0.1986

At 95% confidence interval level of significance = α = 0.05

Critical value of t using excel formula =T.INV.2T(0.05,19)

tc = 2.093

The 95% confidence for the population mean μ is computed using the following formula.

95% confidence interval of the true mean dispensed by the machine is

confidence interval refers to the probability that a population parameter will fall between two set values. So here it means for 95% confidence interval the population mean of soft drink dispense can fall in between of 7.752 ounces to 7.938 ounces.

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