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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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