Give a couple of examples of categorical data arising in a medical research when the disease outcomes and patient characteristics are recorded:

(2)In a research study, in the simplest settings, when an outcome is recorded as success/failure, or, yeso, the outcomes is known as the ____________outcome.

(3)A _____________________distribution is typically used for statistical model in this setting.

(4)Regarding the notation--in this context of working with the binary variables, the symbol "p" does a double duty. pis the standard notation for a _______________ ____________________ and for _________________________.

(5)The symbol for the unknown population proportion is p and the symbol () is used for the ____________________________________

(6)If 21 out of 52 patients in a study show favorable response to a particular regimen, the proportion of the patients who showed favorable response is:_____________or _______%

(7) Is the proportion calculated in (6) above, a population proportion (p), or a sample proportion ()?

(8) Suppose the number of patients participating in a study is "n"(which is the number of trials), and the number of patients who response to the therapy is "X" (which is the number of successes), the sample proportion =

(9)If the sample proportion is nearly normally distributed, ________________approximation to Binomial can be used to conduct the inference.

(10) __________________ inference based on the Binomial Distribution is used when X does not havean approximately normal distribution.

(11)What are the two conditions for the sampling distribution of being nearly normal?

(12) If the two conditions are met, then the sampling distribution of is approximately normal with mean p and standard error determined by what formula?(note: standard error is another name for the standard deviation of the sampling distribution of)

Confidence Interval for Proportions with Minitab:

(13) Construct a 95% confidence interval if is 0.48 and the sample size is 250.

(Note, = X, so, if we multiply by n on both sides, we get X= n*, n represents the number of trials and X represents the number of successes or the events)

we will use Minitab for this)

Step 1, calculate n*and n**(1-)

Step 2. Check to see if the success failure condition is satisfied, i.e. are the values of n*and n**(1-)? 10?

(In Minitab, use the Normal approximation method if both n*, and n**(1-) are ? 10, if not use the Exact Method)

Step 3. Minitab> Stat>Basic Statistics> 1 Proportion> Summarized Data> No. of events (in this case it is n*= 120)>No. of trials >250>Options>Confidence Interval 95%> Method>Normal approximation>OK>OK

\fOne-Sample Proportion X Summarized data Number of events: 120 Number of trials: 250 Perform hypothesis test Hypothesized proportion: Select Options. Help OK CancelOne Sample ProgortionOne-Sample Proportion: Options Confidence level: 95.0 Alternative hypothesis: Fapportion > hypothesized proportion Method Normal apprendimation Help Cancel