Question

Minimally invasive procedures (requiring only small incisions) attempt to reduce the damage to human tissue that results from performing surgery. These procedures typically require small “ports” from which the surgeon inserts thin tubes called trocars. Specialized surgical equipment and miniature camera(s) are then placed through the trocars to conduct the surgery, resulting in less tissue damage than traditional “open” surgeries (which may require a large incision). There are even minimally invasive surgical procedures that can be performed almost exclusively through a single point of entry (i.e., requiring only one small incision).

Minimally invasive procedures have been shown to have equivalent outcomes to traditional surgeries while also reducing human tissue damage. It has also been hypothesized that such minimally invasive procedures reduce the length of hospitalization, with corresponding reductions in postoperative bleeding, scarring, and patient-reported pain.

For a particular type of traditional “open” surgery, the average length of hospitalization following the procedure is 5.8 days.

A random sample of 36 patients needing this particular type of surgery agreed to minimally invasive techniques for the surgical procedure. Using a 1% significance level, test the claim that the mean length of hospitalization (days) is less than that of the traditional “open” surgery (i.e., less than 5.8 days).

a. Using proper notation, write out the null and alternative hypotheses for this test:

H_o:

H₁:

b. Specify what type of statistical procedure would have been utilized for this particular analysis (e.g., two tailed, one sample z-test).

c. If appropriate for the statistical procedure, what would the degrees of freedom (df) be?

d. Assume that the reported test statistic for the analysis was t = - 6.215 with a corresponding p-value less than .0001. In one to two complete sentences, what can you conclude from the test results provided?

Answer 1

a. We are testing,

H0: u= 5.8 vs H1: u<5.8

b. Since the population s.d of the time of hospitalization following the surgery is not given, we we will be using a one sample t test. (AsuumiAs the sample mean and s.d is normally distributed)

c. The appropriate degrees of freedom= n-1 ie 35 here.

d. Since the p-value of our test statistic is significantly less than 1%, we have sufficient evidence to reject H0 at the 1% level and conclude that the mean length of hospitalization is less than 5.8 days.