Question

A. A stress analysis was conducted on random samples of epoxy-bonded joints from two species of wood. A random sample of 120 joints from species A had a mean shear stress of 1250 psi and a standard deviation of 350 psi, and a random sample of 90 joints from species B had a mean shear stress of 1400 psi and a standard deviation of 250 psi. (i) Conduct a hypothesis test with α = 0.02 to determine whether or not there is a difference between the mean sheer stress of the two species of wood. Be sure to state your hypotheses, test statistic, p-value, and conclusions. (ii) Construct a 98% two-sided confidence interval for the difference µA − µB. Compare the CI with the results of the hypothesis test in (i). Are the conclusions consistent?

B. In a test of the effect of dampness on electric connections, 100 electric connections were tested under damp conditions and 150 were tested under dry conditions. Twenty of the damp connections failed and only 10 of the dry ones failed. (i) Conduct a hypothesis test with α = 0.10 to determine whether or not there is a greater proportion of connections which fail under damp conditions compared to dry conditions. Be sure to state your hypotheses, test statistic, p-value, and conclusions. (ii) Construct a 90% two-sided confidence interval for the difference of proportions πdamp −πdry. Compare the CI with the results of the hypothesis test in (i). Are the conclusions consistent?

Answer 1

A:

Let sample 1 shows the sample of species A and sample 2 shows the sample of species B

(i)

Conclusion : There is evidence to conclude that there is a difference between the mean sheer stress of the two species of wood.

(ii)

Since confidence interval does not contain zero so we reject the null hypothesis on the basis of confidence interval.

(iii)

Yes results are consistent.

(B)

(i)

Conclusion: There is evidence to conclude that there is a greater proportion of connections which fail under damp conditions compared to dry conditions

(ii)

Since confidence interval does not contain zero and all values are greater than zero so we reject the null hypothesis on the basis of confidence interval.

(iii) Yes conclusion are consistent.

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