## Question

###### 4* When 308 college students are randomly selected and surveyed, it is found that 129 own...

4* When 308 college students are randomly selected and surveyed, it is found that 129 own a car. Find a 95% confidence interval for the true proportion of all college students who own a car. O 0.363 <p <0.473 O 0.310 < p < 0.434 30.364 < p < 0.474 0.362 < p < 0.474

## Answers

The correct option is C

Solution: We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases: 129 Favorable Cases X = Sample Size N = 308 The sample proportion is computed as follows, based on the sample size N = 308 and the number of favorable cases X = 129: X N 129 308 -0.419 The critical value for a = = 0.05 is c = 21-4/2 = 1.96. The corresponding confidence interval is computed as shown below: CI(Proportion) p(1-P) p(1-P) C -- + n n 0.419 1.96 x 0.419(1 -0.419) , 0.419 +1.96 308 V 0.419(1 -0.419) 308 (0.364, 0.474) Therefore, based on the data provided, the 95% confidence interval for the population proportion is 0.364 <p<0.474, which indicates that we are 95% confident that the true population proportion p is contained by the interval (0.364, 0.474).

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