(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

Stat Graph View Help Assistant Additional Tools Basic Statistics Display Descriptive Statistics.. Regression Store Descriptive Statistics. ANOVA Graphical Summary.. DOE 7 1-Sample Z Control Charts 1-Sample t-. Quality Tools 2-Sample t.. Reliability/Survival Paired t... Predictive Analytics 1 Proportion. Multivariate 2 Proportions.. Time Series 1-Sample Poisson Rate.. Tables Ihad 2-Sample Poisson Rate.. Nonparametrics 1 Variance\fOne-Sample Proportion: Options Confidence level: 95.0 Alternative hypothesis: Proportion *hypothesized proportion Method: Normal approximation Help OK Cancel\fOne-Sample Proportion: Options Confidence level: 95.0 Alternative hypothesis: Proportion > hypothesized proportion Method: Normal approximation Help OK Cancel\f