The tensile strength of Portland cement is being studied. Four different mixing techniques can be used economically. A completely randomized experiment was conducted and the following data were collected: Mixing Technique | Tensile Strength (lb/in²) 1 | 3129 3000 2865 2890 2 | 3200 3300 2975 3150 3 | 2800 2900 2985 3050 4 | 2600 2700 2600 2765 (a) Test the hypothesis that mixing techniques affect the strength of the cement. Use ? = 0.5. (b) Use the tukey's test with ? = 0.5 to make comparisons between pairs of means. (c) Construct a normal probability plot of the residuals. What conclusion would you draw about the validity of the normality assumption? (d) Plot the residuals versus the predicted tensile strength. Comment on the plot.
Added by Luis P.
Close
Step 1
Step 1: Organize the data We have 4 mixing techniques and 4 data points for each technique: Technique 1: 3129, 3000, 2865, 2890 Technique 2: 3200, 3300, 2975, 3150 Technique 3: 2800, 2900, 2985, 3050 Technique 4: 2600, 2700, 2600, 2765 Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 71 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
Samriddhi S.
The compressive strength of concrete is being studied. Four different mixing techniques are being investigated. The following data have been collected: Mixing Technique Compressive Strength (psi) 1 2600 2700 2600 2765 2 2800 2900 2985 3050 3 3200 3300 2975 3150 4 3129 3000 2865 2890 a) Perform the analysis of variance at ̑̑ = 0.05 level of significance. b) Use Tukey's test to make comparison between pairs of means. Estimate the treatment effects. c) Analyze the residuals from the experiment. Draw the normal probability plot. d) Comment on the results.
Madhur L.
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ=60. Let μ denote the true average compressive strength. 1) What are the appropriate null and alternative hypotheses? (4 credits) 2) Let X̄ denote the sample average compressive strength for n=25 randomly selected specimens. Consider the test procedure with test statistic itself (not standardized). If X̄=1340, should H0 be rejected using a significance level of 0.01? [Hint: What is the probability distribution of the test statistic when H0 is true?] (5 credits)
Federico C.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD