Question

A quality control inspector is interested in comparing two concreting companies with respect to overall quality of their work. One measure of quality is whether or not the concrete that has been poured is at least 15 centimeters (cm) thick. The inspector has recorded details for jobs from both companies and is now interested in whether the companies differ with respect to this measure of quality. Let p1 denote the true proportion of times that Company 1 will fail to pour concrete at least 15 cm thick and similarly let p2 denote the proportion for Company 2. The data collected for Company 1 shows that out of 120 jobs measured, 14 of these were less than 15 cm thick. For Company 2, 21 jobs out of 85 resulted in concrete less than 15 cm thick.

(a) Carry out a hypothesis test comparing the two proportions by using the R function prop.test. From the R output report the following:

i. The estimates to p1 and p2.

ii. The approximate 95% confidence interval for p1 − p2.

iii. The p-value for the test comparing p1 and p2.

(b) State the p-value you reported above, can you reject that the proportions are equal at the 5% level of significance? Explain.

(c) Does your confidence interval suggest that one company performs better than the other with respect to this measure of quality? If so, which company performs better and why? If not then clearly explain why this is the case.

(d) Provide a simple statement that summarises the findings you have reported above.

Answer 1

a) R-code:

i) 1st sample proportion p1 = 0.1167

2nd sample proportion p2 = 0.2471

ii) The 95% confidence interval for p1 − p2 is ( -0.23858636, -0.02219796)

iii) p-value = 0.01451

b) Since P-value < alpha 0.05 so we reject H0

Thus we conclude that there is significance difference between the two proportions

c) Zero is not contained in the interval so we reject H0

Thus we conclude that there is significance difference between the two proportions

d) As per confidence interval, Company 2 shows less quality standard maintained compare to Company 1

since the values of confidence interval are less than 0