A recent study states that moonlight can affect the survival rate of new plants. It reported that 26 of 50 plants that were shielded from moonlight survived and 19 of 65 plants left unshielded survived. Choose the 95% confidence interval that represents the difference between the proportions of shielded and unshielded new plants that survive.

And the 95% confidence interval would be given (0.0508;0.405).  

We are confident at 95% that the difference between the two proportions is between

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

represent the real population proportion of shielded survived

represent the estimated proportion of shielded survived

is the sample size required of shielded survived

represent the real population proportion for unshielded survived

represent the estimated proportion for unshielded survived

is the sample size required for unshielded survived

represent the critical value for the margin of error  

Solution to the problem

The population proportion have the following distribution  

The confidence interval for the difference of two proportions would be given by this formula  

For the 95% confidence interval the value of and , with that value we can find the quantile required for the interval in the normal standard distribution.  

And replacing into the confidence interval formula we got:  

And the 95% confidence interval would be given (0.0508;0.405).  

We are confident at 95% that the difference between the two proportions is between