Answered: Fiber and breakfast cereal - In an…

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

Related questions

Concept explainers

Question

I need help with question 6, 8 and 10 plz.

Transcribed Image Text:Fiber and breakfast cereal - In an attempt to learn whether cereals high in fiber are also high in sugar and calories, three researchers took a random sample of 23 brands of breakfast cereal and recorded the calories, sugar (in grams), and fiber (in grams) per serving for each brand. The researchers constructed a linear model using Fiber as the explanatory variable and Calories as the response variable to answer the question, "Can the amount of fiber per serving be used predict the amount of calories per serving in a given brand of cereal?" A scatterplot is given below. Cereal Fiber and Calories 4 6 8. 10 12 Fiber (grams) per serving A linear model is fitted to the data using the statistical software, R, and a summary of that model fit is given below: Coefficients Estimate Std Error t value Pr( > [t]) (Intercept) 118.5 4.057 29.215 1.72e-18 Fiber -4.655 0.8245 -5.645 1.33e-05 Residual standard error: 13.536 on 21 degrees of freedom Multiple R-squared: 0.6028, Adjusted R-squared: 0.5839 Round all calculated answers to 4 decimal places. Calories per serving 120 140 001 09 08

Transcribed Image Text:3. Each additional 1 gram of fiber is associated with a(n) decrease of 4.655 calories per serving. 4. What is the expected amount of calories per serving for a cereal with 0 grams of fiber? 118.5 5. The packaging for the cereal Original Oat Bran has 10 grams of fiber per serving. Calculate the expected value for the number of calories per serving of Original Oat Bran that is predicted by the linear model . expected value = 71.95 6. The packaging for Original Oat Bran indicates it has 70 calories per serving. Use this information and your result from part 5 to calculate the residual for this brand of cereal. residual = 4.1 7. What are the null and alternative hypotheses to test if there is a linear relationship between the X variable and the Y variable in this scenario? OA. Ho : b1 = 0 vs. HA : bị #0 В. Но : В — bi vs. Ha : Bi bi ос. Но : Ві — 0 vs. HA : Bi +0 D. Ho : B1 = 0 vs. HA : B1 > 0 8. What is the test statistic and p-value from the test in part 7? Test statistic: -6.786 and p-value: 1.0306 9. What do the results of the hypothesis test tell us about the linear relationship between the amount of fiber per serving and the calories per serving in breakfast cereal? OA. There is extremely strong evidence to say that there is a linear relationship between fiber and calories in breakfast cereal. B. There is extremely strong evidence to say that there is no linear relationship between fiber and calories in breakfast cereal. C. There is little evidence to say that there is a linear relationship between fiber and calories in breakfast cereal. D. There is little evidence to say that there is no linear relationship between fiber and calories in breakfast cereal. 10. Calculate a 99% confidence interval for the slope, B1, of the regression line predicting the number of calories per serving from the number of grams of fiber per serving. IMPORTANT! You MUST use a t* value rounded to EXACTLY 3 decimal places in this calculation. Round your final answers to 4 decimal places.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions