An experimental surgical procedure is being studied as an alternative to the old
ID: 2934463 • Letter: A
Question
An experimental surgical procedure is being studied as an alternative to the old method. Both methoo are considered safe. Five surgeons perform the operation on two patients matched by age, sex, and other relevant factors, with the results shown below. The time to complete the surgery (in minutes) is recorded. At the.01 significance level, is the new way better? surgeon 4 40 32 Surgeon 36 1 --i surgeon 2--Surgeon3, 38 Surgeons Old way New w 62 56 42 30 7. The variable of interest (x) in this problem is: a. b. c. d. e None of the above Surgeons Surgical procedure Time to complete surgery (in minutes) New Way and Old Way 8. The problem involves a. Comparing the proportions of two populations b. Comparing the variances of two populations Comparing the means of two dependent populations Comparing the means of two independent populations None of the above c. d. e. f the difference in time to complete the surgery is computed as Old Way minus New Way, the appropriate pair of hypotheses is: a. Ho: 20 H1: a2, b. Reject Ho if t > lan-, c. Reject Ho ift - 11. What is the computed statistic equal to? 12. At0.01 significance level, which of the following statements would be the most appropriate given the statistical result from the sample? a. There is no difference in the average time to complete the surgery between the surgeons There is a difference in the average time to complete the surgery between the surgeons There is no difference in the average time to complete the surgery between the two surgical methods There is a difference in the average time to complete the surgery between the two surgical methods - the new way is better There is a difference in the average time to complete the surgery between the two surgical methods-the old way is better d. e. In 1999, a sample of 400 in store shoppers showed that 184 paid by debit card. In 2013, a sample of the same size showed that 300 paid by debit card. Formulate the appropriate hypotheses to test whether the percentage of the debit card shoppers has increased. Carry out the test at the 0.01 significance level. The problem involves: a. Comparing the proportions of two populations b. Comparing the variances of two populations c. Comparing means of two independent populations d. Comparing the means of two dependent samples e. None of the above 13.Explanation / Answer
Q>7 Variable of interest here are Time to complete surgery
Q.8 THe problem involved "Comparing the means of two dependent populations". Dependet because here experiment is done on the same person two times.
Q.9. H0 : = 0 ; Ha : > 0
Q.10 Decision rule is
Reject H0 if t > ta/2 .n-1 Option b is correct.
Q.11 Test statistic
Average of difference of mean = 8.4
Standard deviation of difference of mean = 2.702
t = dbar / (sd / sqrt(n) = 8.4/ (2.702 / sqrt(5)) = 6.95
Here t > tcritical (which is for dF = 4 and alpha = 0.01 is tcr = 4.6041) so we shall reject the null hypothesis and can conclude that there is difference in the average time and new way is better (option D is correct)
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