Question

Problem 2) A coffee machine dispenses coffee into paper cups. You’re supposed to get 10 ounces of coffee, but the amount varies slightly from cup to cup. The amounts in ounces measured in a random sample of 20 cups are given in the Excel file, tab coffee machine.

a) For one experimental unit, what is the response variable? Categorical or quantitative?

b) Verify the two conditions for using the normal distribution for the sample mean:  Random sample?  Is n ≥ 30 or is x approximately normally distributed or have no extreme asymmetry or outliers? The histogram of the data is given. (Hint: yes, the data are approximately normal.)

c) Calculate using Excel or StatKey (NOT by hand)  ?̅, the mean amount  s, the standard deviation Remember when you paste data into StatKey, be sure that you paste only numbers and leave these unchecked.

X-bar=9.845 S=0.199

d) Conduct a significance test to determine if there is evidence that on average the machine is shortchanging customers. Use the sample mean ?̅and sample standard deviation that you calculated previously to calculate the test statistic. State the conclusion in the context of the problem.

Answer 1

a) quantitative

Two types of variables are used in statistics:Quantitative and categorical (also calledqualitative): Quantitative variables are numerical variables: counts, percents, or numbers. Categorical variables are descriptions of groups or things, like “breeds of dog” or “voting preference”

(d) here we use t-test with

null hypothesis H0:=10 and

alternat hypothesis Ha:<10

and statistic t=(?̅-)/(s/sqrt(n))=(9.845-10)/(0.199/sqrt(20))=-3.48

the typical one-tailed critical t(0.05,19)=2.09 is less than absolute value of calculated t=3.48, so we reject H0 and conclude that there is evidence that on average the machine is short changing customers.