Question

It takes an average of 11 minutes for blood to begin clotting after an injury. An EMT wants to see if the average will decline if the patient is immediately told the truth about the injury. The EMT randomly selected 68 injured patients to immediately tell the truth about the injury and noticed that they averaged 10 minutes for their blood to begin clotting after their injury. Their standard deviation was 3.3 minutes. We let α = 0.01 be the level of significance level of significance.

(a) For this study, should we use a (i) z-test for proportion estimate or (ii) t-test for a population mean?

(b) What would the null hypothesis be?

(c) What would the alternative hypothesis be?

(d) What is the p-value (rounded to 4 decimal places)?

(e) Based on this, should we reject the null hypothesis? Explain your answer in terms of α and p.

(f) Thus, the final conclusion is that

i. The data suggest the population mean is significantly less than 11 at α = 0.01, so there is statistically significant evidence to conclude that the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is less than 11.

ii. The data suggest that the population mean is not significantly less than 11 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is less than 11.

iii. The data suggest the population mean is not significantly less than 11 at α = 0.01, so there is statistically significant evidence to conclude that the population mean time for blood to begin clotting after an injury if the patient is told the truth immediately is equal to 11.

Answer 1