In Exercises 10.25-10.30, hypothesis tests are proposed. For each

hypothesis test,

a. identify the variable.

b. identify the two populations,

c. determine the null and alternative hypotheses.

d. classify the hypothesis test as two-tailed, left-tailed, or right-tailed.

Neurosurgery Operative Times. An Arizona State University professor, R. Jacobowitz, Ph.D., in consultation with G. Vishtch, M.D., and other neurosurgeons obtained data on operative times, in minutes, for both a dynamic system (Z-plate) and a static system (ALPS plate). They wanted to perform a hypothesis test to decide whether the mean operative time is less with the dynamic system than with the static system.

We are given a hypothesis.

A hypothesis test is performed to decide whether the mean operative time is less with the dynamic system than with the static system.

A variable is an attribute or a characteristic that can be measured. The value of the variable may differ for each and every unit. That is, a variable is defined as the characteristic which is recorded for each case.

In this study, neurosurgery operative times is recorded for different systems. So the variable is neurosurgery operative times.

The population includes all the individuals of interest that are being examined. In other words, the collection of all people, items, or objects that are required for a specific study is defined as the population.

Neurosurgery operative times are recorded for two systems when the operation is done on a dynamic system and when the operation is done on a static system.

So the two populations are neurosurgery operation of a dynamic system and neurosurgery operation of a static system.

Let us assume ${\mu }_1$denotes the mean operative time of dynamic system and ${\mu }_2$denotes the mean operative time of static system.

The null hypothesis is defined as

$H_0:$There is no significant difference between the mean operative time of dynamic system and static system.

role="math" localid="1652779036248" $H_0:{\mu }_1={\mu }_2$

The alternative hypothesis is defined as

$H_a:$The mean operative time is less with the dynamic system than with the static system.

$H_a:{\mu }_1<{\mu }_2$

As our alternative hypothesis suggest that the mean of the first population is less than the mean of the second population.

So the hypothesis can be classified as left-tailed test.