Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The games of fat per serving are as follows 8,8,11,7,9,9. Assume the underlying distribution is approximately normal. Note: if you’re 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.) a) Construct a 95% 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 two decimal points.)(__________ , ___________) (ii)Sketch the graph (iii)Calculate the error bound. (round your answers two decimal points.) b) 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? Decrease the sample size Increase the sample size Determine the population standard deviation Nothing can be changed to guarantee a smaller error boundthe image I added is for part a (ii) The image shows a bell curve, representing a normal distribution, along with a confidence interval. Here's a detailed explanation:1. **Bell Curve**: The central graph is a bell-shaped curve depicting a normal distribution. It is symmetric around the center.2. **Confidence Interval**: The horizontal line beneath the curve represents the confidence interval, spanning from one tail of the distribution to the other under the curve.3. **Alpha (α) Levels**: - On each side of the curve, there are arrows pointing to the tails labeled as $\alpha/2 =$. These indicate the areas in the tails of the distribution that are not included in the confidence level. - The area under the tails adds up to the significance level ($\alpha$), which is typically a small percentage like 5% or 1%.4. **Confidence Level (C.L.)**: - The center of the curve is labeled as "C.L. = ", suggesting the confidence level, which is the probability that a parameter will fall within the interval estimate. - For example, a 95% confidence level would imply that the central 95% of the distribution is shaded under the curve, while the 5% is split between the two tails.5. **Label 'p'**: Below the distribution line, there is a label "p'", indicating the point estimate or sample proportion corresponding to the center of the confidence interval.This diagram is typically used in statistics to illustrate the concept of confidence intervals and hypothesis testing, showing how sample data might be used to estimate population parameters and the uncertainty associated with these estimates.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The games of fat per serving are as follows 8,8,11,7,9,9. Assume the underlying distribution is approximately normal.

Note: if you’re 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.)

a) Construct a 95% 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 two decimal points.)

(__________ , ___________)

(ii)Sketch the graph

(iii)Calculate the error bound. (round your answers two decimal points.)

b) 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?

Decrease the sample size
Increase the sample size
Determine the population standard deviation
Nothing can be changed to guarantee a smaller error bound

the image I added is for part a (ii)

The image shows a bell curve, representing a normal distribution, along with a confidence interval. Here's a detailed explanation:

1. **Bell Curve**: The central graph is a bell-shaped curve depicting a normal distribution. It is symmetric around the center.

2. **Confidence Interval**: The horizontal line beneath the curve represents the confidence interval, spanning from one tail of the distribution to the other under the curve.

3. **Alpha (α) Levels**:
- On each side of the curve, there are arrows pointing to the tails labeled as $\alpha/2 =$. These indicate the areas in the tails of the distribution that are not included in the confidence level.
- The area under the tails adds up to the significance level ($\alpha$), which is typically a small percentage like 5% or 1%.

4. **Confidence Level (C.L.)**:
- The center of the curve is labeled as "C.L. = ", suggesting the confidence level, which is the probability that a parameter will fall within the interval estimate.
- For example, a 95% confidence level would imply that the central 95% of the distribution is shaded under the curve, while the 5% is split between the two tails.

5. **Label 'p'**: Below the distribution line, there is a label "p'", indicating the point estimate or sample proportion corresponding to the center of the confidence interval.

This diagram is typically used in statistics to illustrate the concept of confidence intervals and hypothesis testing, showing how sample data might be used to estimate population parameters and the uncertainty associated with these estimates.

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