Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 7; 7; 11; 6; 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.)Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets. (i) State the confidence interval. (Round your answers to two decimal places.)

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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: 7; 7; 11; 6; 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.)Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.

(i) State the confidence interval. (Round your answers to two decimal places.)
### Confidence Interval for Population Mean

#### Part (a)

**Task:** Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets.

(i) **State the confidence interval.**  
(Round your answers to two decimal places.)

- ( ____ , ____ )

(ii) **Sketch the graph.**

The graph is a bell curve representing a normal distribution. It shows a confidence level (C.L.) of 0.90 in the center section, with \( \alpha/2 \) regions on both tails indicating the level of significance not included in the confidence interval. The mean \(\bar{X}\) is located at the center. There are blanks on the graph denoting areas where values need to be filled in.

- \( \frac{\alpha}{2} = \) ___
- C.L. = 0.90
- \( \frac{\alpha}{2} = \) ___

(iii) **Calculate the error bound.**  
(Round your answer to two decimal places.)

- Error bound: ___

#### Part (b)

**Question:** If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?
Transcribed Image Text:### Confidence Interval for Population Mean #### Part (a) **Task:** Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets. (i) **State the confidence interval.** (Round your answers to two decimal places.) - ( ____ , ____ ) (ii) **Sketch the graph.** The graph is a bell curve representing a normal distribution. It shows a confidence level (C.L.) of 0.90 in the center section, with \( \alpha/2 \) regions on both tails indicating the level of significance not included in the confidence interval. The mean \(\bar{X}\) is located at the center. There are blanks on the graph denoting areas where values need to be filled in. - \( \frac{\alpha}{2} = \) ___ - C.L. = 0.90 - \( \frac{\alpha}{2} = \) ___ (iii) **Calculate the error bound.** (Round your answer to two decimal places.) - Error bound: ___ #### Part (b) **Question:** If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before it was done?
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