30 randomly selected cans of Coke are measured for the amount of cola in ounces. The sample values have a mean of 12.18 ounces and a standard deviation of 0.118 ounces.
The 99% confidence interval is ( ounces, ounces). Round each result to two decimal places.
99% = mean ± 2.575 SEm
SEm = SD/√n
To determine the 99% confidence interval for the mean amount of cola in ounces, we can use the formula:
Confidence Interval = (sample mean) ± (critical value) * (standard deviation / square root of sample size)
Step 1: Find the critical value
The critical value corresponds to the desired level of confidence and the sample size. In this case, we want a 99% confidence interval and have a sample size of 30. We can use a Z-table or a calculator to find the critical value.
Using a Z-table, the critical value for a 99% confidence interval is approximately 2.576.
Step 2: Calculate the confidence interval
We are given that the sample mean is 12.18 ounces and the standard deviation is 0.118 ounces. The sample size is 30.
Confidence Interval = (12.18) ± (2.576) * (0.118 / √30)
Calculating the standard error:
Standard Error = standard deviation / √sample size = 0.118 / √30 ≈ 0.0215
Confidence Interval = (12.18) ± (2.576) * (0.0215)
Calculating the upper and lower limits of the interval:
Lower Limit = 12.18 - (2.576 * 0.0215) ≈ 12.18 - 0.0554 ≈ 12.12
Upper Limit = 12.18 + (2.576 * 0.0215) ≈ 12.18 + 0.0554 ≈ 12.24
Rounding the final results to two decimal places:
The 99% confidence interval is (12.12 ounces, 12.24 ounces).