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.

Solution Steps

We have a sample of 16 people with the following statistics:

• Sample Mean (\( \bar{x} \)) = 2.6 cups
• Sample Standard Deviation (\( \sigma \)) = 1.5 cups
• Sample Size (\( n \)) = 16
• Confidence Level = 95%

For a 95% confidence level, the Z-Score (\( Z \)) is approximately 1.96.

The formula for the margin of error (\( E \)) is given by:

\[ E = \frac{Z \times \sigma}{\sqrt{n}} \]

Substituting the known values:

\[ E = \frac{1.96 \times 1.5}{\sqrt{16}} = \frac{1.96 \times 1.5}{4} \]

Calculating the margin of error:

\[ E = \frac{2.94}{4} = 0.735 \]

Rounding to two decimal places, we find:

\[ E \approx 0.73 \]

Final Answer