### Confidence Interval Calculation for Sodium Levels in Bread**Problem Statement:**A company that produces white bread is concerned about the distribution of the amount of sodium in its bread. The company takes a simple random sample of 100 slices of bread and computes the sample mean to be 103 milligrams of sodium per slice.**Objective:**Construct a 96% confidence interval for the unknown mean sodium level, assuming that the population standard deviation is 10 milligrams.**Mathematical Formulation:**We aim to find the confidence interval \(CI\) such that:\[ \text{Lower Limit} < \mu < \text{Upper Limit} \]Given:- Sample Size (\(n\)) = 100- Sample Mean (\(\bar{x}\)) = 103 mg- Population Standard Deviation (\(\sigma\)) = 10 mg- Confidence Level = 96%The formula for the confidence interval for the mean when the population standard deviation is known is:\[ \bar{x} \pm Z_{\alpha/2} \left( \frac{\sigma}{\sqrt{n}} \right) \]1. Determine the Z-value: - Since the confidence level is 96%, the significance level (\(\alpha\)) is 4%, or 0.04. - Thus, \(\alpha/2 = 0.02\). - For a 96% confidence level, the Z-value is approximately 2.05 (can be found from Z-tables or standard statistical tools).2. Compute the margin of error (ME):\[ ME = Z_{\alpha/2} \left( \frac{\sigma}{\sqrt{n}} \right) = 2.05 \left( \frac{10}{\sqrt{100}} \right) = 2.05 \times 1 = 2.05 \]3. Calculate the confidence interval limits: - Lower Limit = \(\bar{x} - ME = 103 - 2.05 = 100.95\) - Upper Limit = \(\bar{x} + ME = 103 + 2.05 = 105.05\)**Result:**\[ 100.9 \, \text{mg} < \mu < 105.1 \, \text{mg} \](Values are rounded to the nearest tenth with one digit after the decimal point,

Sample size: Sample mean: mgPopulation standard deviation: mgConfidence level:

Answered: A company that produces white bread is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A physicist examines 4 seawater samples for lead concentration. The mean lead concentration for the sample data is 0.890 cc/cubic meter with a standard deviation of 0.0312. Determine the 80 % confidence interval for the population mean lead concentration. Assume the population is approximately normal. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Aisha wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 44 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 5.1 and a standard deviation of 3.5. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to 3 decimal places. Assume the data is from a normally distributed population. Round answers to 3 decimal places where possible.
How large of a sample is required for a to construct a 99% confidence interval around a mean with an error of less than 1.5. Assume the standard deviation is 42.
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles cola has a mean caffeine content of 57.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.9 milligrams. At a = 0.04, can you reject the company's claim? Complete parts (a) through (e). C (a) Identify Ho and H₂. Choose the correct answer below. OA. Ho: 257.4 OB. Ho: H=57.4 H_:μ#57.4 H₂H<57.4 C. Ho: H=55 H₂:μ#55 OD. Ho: μ255 H:H<55 OE. Ho: 57.4 OF. Ho: *55 H₂:μ=57.4 Ημ= 55 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical values are ± 2.05. OB. The critical value is. Identify the rejection region(s). Choose the correct answer below. OA OB. O C. O Fail to reject Ho Fail to reject Ho Fail to reject Ho Q X…
Mrs. Gallas wanted to estimate the average weight of an Oreo cookie to determine if theaverage weight was less than advertised. She selected a random sample of 30 cookies andfound the weight of each cookie (in grams). The mean weight was = 11.1921 grams with astandard deviation of sx = 0.0817 grams. Make a 95% confidence interval to estimate the truemean weight of an Oreo. 1. What is the formula for calculating the standard deviation of the sampling distribution of x? 2.What condition must be met to use this formula? Has it been met?
A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 57.4 milligrams. Assume the population is normally distributed and the population standard deviation is 6.9 milligrams. At a=0.04, can you reject the company's claim? Complete parts (a) through (e). (a) Identify Ho and H₂. Choose the correct answer below. OA. Ho: 257.4 H₂:μ< 57.4 OB. Ho: H=57.4 H₂:μ*57.4 C. Ho: H=55 H₂:55 OD. Ho: 255 H₂H<55 OE. Ho: 57.4 Η μ = 57.4 OF. Ho: *55 H₂: H=55 (b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to two decimal places as needed.) A. The critical values are ± OB. The critical value is
Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). ANOVA table Source SS df MS F Regression 1,810.5782 1 1,810.5782 38.54 Residual 1,315.4934 28 46.9819 Total 3,126.0716 29 Regression output Variables Coefficients Standard Error t(df=28) Intercept 14.62785 3.1572 3.178 Distance–X 5.1603 0.8312 6.21 Click here for the Excel Data File a-1. Determine the regression equation. (Round your answers to 3 decimal places.) a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage? b. How much damage would you…
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 4 points with 99% confidence assuming s=10.7 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence assuming s=13.4 based on earlier studies? Suppose the doctor would be content with 95% confidence. How does the decrease in confidence affect the sample size required?
An industrial engineer is conducting a time study for a work element. The select time is 4.5 minutes, and the sample standard deviation of the observed time is 20 seconds. What is the appropriate sample size if the estimate is to be 5 percent of the true average time 95 percent of the time?
The president of a large university wishes to compare the standard deviation of the ages of students presently enrolled to previous years. The distribution of ages has been approximately normal. Find the 90% confidence interval for the population standard deviation of the student ages of the University. A random sample of 20 university students has a standard deviation of 6.1 years in a mean of 23.8 years what is the confidence interval of the population standard deviation?
Suppose we have data coming from 69 i.i.d) observations. The sample mean is JÓ28 and the sample standard deviation is calculated to be 1.63. Find a 95% confidence interval for the true mean.

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS