Question

The Dispenser Right Company makes a soft drink dispensing machine used in many fast food restaurants. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by a particular machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed: 14.25​13.70​14.02 14.13​13.99​14.04 A) What is the 99% confidence interval? B) In order to be 99% accurate to within 0.02 ounces, what sample size would be needed if the sample standard deviation is 0.18? C) What are the correct null and alternative hypotheses are D) What is the correct value of the test statistic? E) At 5%, what conclusion we make about the null hypothesis?

Answer 1

Given data,

Sample size n=6

Sample data = {14.25, 13.70, 14.02, 14.13, 13.99, 14.04}

From the sample data,

Mean of given sample = 14.0217

Variance = 0.0337

Standard deviation = variance = 0.1836

a) To find, 99% confidence level

t-score at 5 degrees of freedom and at 0.01 level of significance t = 4.032

99% confidence interval for mean is as follows

b) Given, sample standard deviation s= 0.18

Margin of Error E = 0.02

Confidence level = 99%

z-score at 99% confidence level z=2.58

We know that Margin of Error