Question

A survey of 500 randomly selected adults found that 57% say that they would take a ride in a fully self-driving car. The 95% confidence interval for the true proportion of all adults who would take a ride in a full self-driving car is found to be (0.5266, 0.6134). Can we conclude that the majority of all adults would take a ride in a fully self-driving car?

Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.

No; The data does not include all adults, so we cannot make a conclusion about the population.

No; The confidence interval limits are not large enough to determine that a majority rely only on cellular phones. The proportion would need to be much greater than 50%, and the one above is only slightly larger.

Yes; Since the proportion of adults who said yes is 57%, and this is higher than 50%, we can conclude that a majority would take a ride in a fully self-driving car.

Answer 1

Here the 95% confidence interval has been formed and see that both the limits of the interval are more than 50%. So with 95% confidence we can say that the required proportion of interest is more than 50%. Hence from an inferential perspective with 95% confidence coefficient we can conclude this but there is chance of error of 5% which we need to keep in mind.

So we can conclude this statement at a level of significance of 5%. But technically in the statement ,the level of significance is not mentioned. So the answer should be the second option that is: No; The data does not include all adults, so we cannot make a conclusion about the population.

(Note: if the instructor didn't mean to say this in such a strich technical manner then go for 1st option. Better to check with the person who gave the question. But if no such information is available then 2nd option should be the answer, technically)

The remaining options are incorrect as this is not how the inference is done.

Hope the solution helps. Thank you.