1.46: A contractor claims that the mean compressive strength for a concrete mix is 5000 psi (μ) and that it has a standard deviation of 400 psi (σ). If you break 20 cylinders (N) and obtain a mean compressive strength of 4,800 psi (m), would you believe the contractor’s claim? Why? (Hint; Use statistical t-test.) Next, what is the maximum number of breaks (N) that could be performed that WOULD make you believe the contractor’s claim? Assume that the results wouldn’t change, i.e. σ = 400 psi and m = 4,800 psi. Recall that the equation to find the lower bound of a one sided distribution is LB = μ - (tσ)* σ/(N^0.5) Because the sample size is relatively small, use the ‘student t test’ to represent the normal distribution. You should have at least 95% confidence in the results. That means that α = 0.05. Keep in mind that this is a one tailed distribution, since we only care about the lower bound (i.e. meaning that we are only concerned about concrete that doesn’t meet our minimum strength requirements). Do not forget to find the appropriate degree of freedom for this test. Use a table found online.
1.46: A contractor claims that the mean compressive strength for a concrete mix is 5000 psi (μ) and that it has a standard deviation of 400 psi (σ). If you break 20 cylinders (N) and obtain a mean compressive strength of 4,800 psi (m), would you believe the contractor’s claim? Why? (Hint; Use statistical t-test.) Next, what is the maximum number of breaks (N) that could be performed that WOULD make you believe the contractor’s claim? Assume that the results wouldn’t change, i.e. σ = 400 psi and m = 4,800 psi. Recall that the equation to find the lower bound of a one sided distribution is LB = μ - (tσ)* σ/(N^0.5) Because the sample size is relatively small, use the ‘student t test’ to represent the normal distribution. You should have at least 95% confidence in the results. That means that α = 0.05. Keep in mind that this is a one tailed distribution, since we only care about the lower bound (i.e. meaning that we are only concerned about concrete that doesn’t meet our minimum strength requirements). Do not forget to find the appropriate degree of freedom for this test. Use a table found online.
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