Questions: A sample of 16 people was conducted to see how many cups of coffee (per day) people buy at star-bucks. The sample had a mean of 2.6 cups and a standard deviation of 1.5 cups. What is the margin of error (step 2 ) for a 95 percent confidence interval?
Note: Round your answer to two decimal places.
Transcript text: A sample of 16 people was conducted to see how many cups of coffee (per day) people buy at star-bucks. The sample had a mean of 2.6 cups and a standard deviation of 1.5 cups. What is the margin of error (step 2 ) for a 95 percent confidence interval?
Note: Round your answer to two decimal places.
Solution
Solution Steps
Step 1: Given Data
We have a sample of 16 people with the following statistics:
Sample Mean (xˉ) = 2.6 cups
Sample Standard Deviation (σ) = 1.5 cups
Sample Size (n) = 16
Confidence Level = 95%
Step 2: Z-Score Calculation
For a 95% confidence level, the Z-Score (Z) is approximately 1.96.
Step 3: Margin of Error Calculation
The formula for the margin of error (E) is given by:
E=nZ×σ
Substituting the known values:
E=161.96×1.5=41.96×1.5
Calculating the margin of error:
E=42.94=0.735
Rounding to two decimal places, we find:
E≈0.73
Final Answer
The margin of error for a 95% confidence interval is \\(\boxed{0.73}\\).