Question

Construct a confidence interval of the population proportion at the given level of confidence. x=120, n=1100, 96% confidence

The upper bound of the confidence interval is?

The lower bound of the confidence interval is?

Answer 1

Upper bound: 0.1284

Lower bound 0.0898

Calculations:

One-Proportion Confidence Interval

We need to construct the 96% confidence interval for the population proportion. We have been provided with the following information: The sample size is N = 1100, the number of favorable cases is X = 120 and the sample proportion is pˉ​=X/N​=120/1100​=0.1091, and the significance level is α=0.04 Critical Value Based on the information provided, the significance level is α=0.04, therefore the critical value is Zc​=2.0537. This can be found by either using excel or the Z distribution table. Margin of Error The confidence interval: Therefore, based on the data provided, the 96% confidence interval for the population proportion is 0.0898<p<0.1284, which indicates that we are 96% confident that the true population proportion p is contained by the interval (0.0898,0.1284)

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