An article describes the results of an experiment. Patients with gluten-related disorders were randomly assigned to one of two groups. One group was a control group who received treatment A. Of the 73 patients in this group, 42 reported improvements at the end of the study period. Those in the second group received treatment B. Of the 98 patients in the supplement group, 69 reported improvements at the end of the study period.
Is it possible to use the large-sample z test and the large-sample z confidence interval to draw conclusions about a difference in treatment proportions? Why?

A)It is possible to use the large-sample z test, because the treatment groups are large enough.It is impossible to use the large-sample z confidence interval to draw conclusions, since patients are randomly assigned to the treatment groups.
B)It is impossible to use the large-sample z test, because the treatment groups are not large enough.But it is possible to use the large-sample z confidence interval to draw conclusions, since patients are randomly assigned to the treatment groups.
C)It is impossible to use both the large-sample z test and the large-sample z confidence interval, since the treatment groups are not large enough, and patients are randomly assigned to the treatment groups.
D)It is possible to use both the large-sample z test and the large-sample z confidence interval, since the treatment groups are large enough, and patients are randomly assigned to the treatment groups.

Question

An article describes the results of an experiment. Patients with gluten-related disorders were randomly assigned to one of two groups. One group was a control group who received treatment A. Of the 73 patients in this group, 42 reported improvements at the end of the study period. Those in the second group received treatment B. Of the 98 patients in the supplement group, 69 reported improvements at the end of the study period. ​
Is it possible to use the large-sample z test and the large-sample z confidence interval to draw conclusions about a difference in treatment proportions? Why?
​
A)It is possible to use the large-sample z test, because the treatment groups are large enough.It is impossible to use the large-sample z confidence interval to draw conclusions, since patients are randomly assigned to the treatment groups.
B)It is impossible to use the large-sample z test, because the treatment groups are not large enough.But it is possible to use the large-sample z confidence interval to draw conclusions, since patients are randomly assigned to the treatment groups.
C)It is impossible to use both the large-sample z test and the large-sample z confidence interval, since the treatment groups are not large enough, and patients are randomly assigned to the treatment groups.
D)It is possible to use both the large-sample z test and the large-sample z confidence interval, since the treatment groups are large enough, and patients are randomly assigned to the treatment groups.

Quizplus · Accepted Answer

The large-sample z test and confidence interval can be used because both treatment groups have a sufficient number of participants (73 and 98, respectively), which meets the common rule of thumb for "large" samples (usually n ≥ 30). Additionally, the random assignment of patients to treatment groups helps to ensure that the results are not biased by pre-existing differences between the groups, making statistical methods like the z test and confidence interval appropriate for analyzing the data.

An Article Describes the Results of an Experiment