B11. The yield ( \( y \) ) of a chemical process is a random variable whose value is considered to be a linear function of the temperature (x). The following data of corresponding values of \( x \) and \( y \) is found: \begin{tabular}{|c|c|c|c|c|c|} \hline \( \mathrm{x} \) & 0 & 25 & 50 & 75 & 100 \\ \hline \( \mathrm{y} \) & 14 & 38 & 54 & 76 & 95 \\ \hline \end{tabular} (a) Construct a scatter plot of the data and fit an appropriate simple linear regression model. (b) Can a significant relationship between yield and temperature be established? [6] (c) Give the \( 95 \% \) confidence interval of the expected yield at a temperature of \( x_{0}=80 \) degrees celsius.
Added by Gannet
Close
Step 1
- The data points are: (0, 14), (25, 38), (50, 54), (75, 76), and (100, 95). Show more…
Show all steps
Your feedback will help us improve your experience
Jainendra Ojha and 98 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
11. The following data represents the yield y of a chemical reaction at various temperatures x : x(F°) y 150 77.4 150 76.7 160 78.2 180 84.5 200 83.9 200 83.7 225 85.6 250 88.9 250 90.3 280 94.8 The summary statistics are: x̄ = 204.5, ȳ = 84.4, sx = 45.7, sy = 5.89, and r = 0.975. a. Find the equation of the regression line of y on x. b. What yield is predicted for the temperature x = 190? c. What is the residual associated with the observation (225, 85.6)? d. The yield is predicted to increase by ___________ for every 1° increase in temperature.
David N.
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 32 31 30 22 32 35 34 35 35 37 24 37 30 28 38 a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total b. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals).
Lucas F.
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 39 35 28 29 36 33 41 39 33 44 28 35 37 32 36 Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Treatments Error Total Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p-value is - Select your answer - What is your conclusion? - Select your answer -
Tanvi G.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Watch the video solution with this free unlock.
EMAIL
PASSWORD