Question

1. A coffee machine dispenses 6 fluid ounces of coffee into a paper cup. Previous studies have shown that the amount dispensed is a normal distribution. A random sample of 15 cups is obtained where the standard deviation, s, is 0.154.

1. Determine if the requirements are met to compute a confidence interval for the true standard deviation, σ, of amounts of coffee being dispensed. List each requirement and state information given to support each one.

2. If the requirements are met, use StatCruch to find a 95% confidence interval and write the interpretation of the confidence interval for the population standard deviation.

Answer 1

1. Determine if the requirements are met to compute a confidence interval for the true standard deviation, σ, of amounts of coffee being dispensed. List each requirement and state information given to support each one.

Conditions for Constructing a Confidence Interval:
1. Random: The data come from a well-designed random sample or randomized experiment.
2. Normal: The sampling distribution of the statistic is approximately Normal.
3. Independent: Individual observations are independent. When sampling without replacement, the sample size n should be no more than 10% of the population size N (the 10% condition) to use our formula for the standard deviation of the statistic.

1. If the requirements are met, use StatCruch to find a 95% confidence interval and write the interpretation of the confidence interval for the population standard deviation.

95% CI for σ using Chi-Square

(0.113, 0.243)

The 95% confidence interval for the standard deviation, σ, of amounts of coffee being dispensed is between 0.113 and 0.243.

We are 95% confidence that the true standard deviation, σ, of amounts of coffee being dispensed is between 0.113 and 0.243.