Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 11; 7; 9; 9. Assume the underlying distribution is approximately normal. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Unitary Method
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![Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 11; 7; 9; 9. Assume the underlying distribution is approximately normal.
**NOTE:** If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
### Part (a)
Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.
1. **(i) State the confidence interval.**
(Round your answers to two decimal places.)
\[ \_\_\_\_\_\_\_ \quad , \quad \_\_\_\_\_\_\_ \]
2. **(ii) Sketch the graph.**
Diagram of a normal distribution curve is present with the central region marked as C.L. (Confidence Level). The tails are labeled with \(\frac{\alpha}{2}\) on each side. An arrow points from each tail end downward toward the horizontal axis, indicating the critical regions. The mean, \(\bar{X}\), is marked centrally on the axis below the curve.
- \( \frac{\alpha}{2} = \_\_\_\_\_\_\_ \)
- \( C.L. = \_\_\_\_\_\_\_ \)
3. **(iii) Calculate the error bound.**
(Round your answer to two decimal places.)
\[ \_\_\_\_\_\_\_ \]
This task involves statistical calculations to establish the confidence interval and error bound, along with an illustration of the confidence interval on a normal distribution curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fbc6c36-d9e9-40b5-b390-5374081e380d%2F77227590-f442-4dc7-b754-96f10bc4d47b%2F047n4bf_processed.jpeg&w=3840&q=75)
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