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 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 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 i attached a picture for the graph (ii) The image depicts a normal distribution curve, often used in statistics to represent a probability distribution.1. **Distribution Curve Explanation:** - The curve represents a normal distribution with a bell shape, indicating that most data points are concentrated around the mean. - The horizontal line beneath the curve represents the range of possible values.2. **Annotations and Symbols:** - **α/2:** These symbols are placed on both tails of the distribution, indicating the significance level divided by two. In hypothesis testing, this represents the probability of the extreme ends, or tails, of the distribution. - **C.L.=** This is placed at the peak of the curve and stands for "Confidence Level." It represents the probability that a parameter lies within a specified interval.3. **Graphical Elements:** - Arrows pointing towards the center of the curve and towards the horizontal line suggest the direction of interpretation for the confidence interval. - Two vertical lines from the tail areas mark the region of rejection in hypothesis testing, signifying where outcomes are considered statistically significant. - The distribution of lines beneath the curve symbolizes the confidence interval range around the central point, labeled as "p'," which typically stands for the sample proportion or mean. This diagram visually represents the concept of confidence intervals and the areas of significance, commonly used in statistical inference and hypothesis testing.

1. (a) To calculate the confidence interval for population mean , let assume that population is…

Answered: Six different national brands of…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 10E

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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 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 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

i attached a picture for the graph (ii)

The image depicts a normal distribution curve, often used in statistics to represent a probability distribution.

1. **Distribution Curve Explanation:**
- The curve represents a normal distribution with a bell shape, indicating that most data points are concentrated around the mean.
- The horizontal line beneath the curve represents the range of possible values.

2. **Annotations and Symbols:**
- **α/2:** These symbols are placed on both tails of the distribution, indicating the significance level divided by two. In hypothesis testing, this represents the probability of the extreme ends, or tails, of the distribution.
- **C.L.=** This is placed at the peak of the curve and stands for "Confidence Level." It represents the probability that a parameter lies within a specified interval.

3. **Graphical Elements:**
- Arrows pointing towards the center of the curve and towards the horizontal line suggest the direction of interpretation for the confidence interval.
- Two vertical lines from the tail areas mark the region of rejection in hypothesis testing, signifying where outcomes are considered statistically significant.
- The distribution of lines beneath the curve symbolizes the confidence interval range around the central point, labeled as "p'," which typically stands for the sample proportion or mean.

This diagram visually represents the concept of confidence intervals and the areas of significance, commonly used in statistical inference and hypothesis testing.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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