A study finds that college students found it unpleasant to sit alone and think.1 The same article describes a second study in which college students appear to prefer receiving an electric shock to sitting in solitude. The article states that "when asked to spend 15 minutes in solitary thought, 12 of 18 men and 6 of 24 women voluntarily gave themselves at least one electric shock." Use this information to estimate the difference between men and women in the proportion preferring pain over solitude. The standard error of the estimate is 0.154.

Assuming a confidence level of 95%.

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.  

The standard error for this case is given by:

And the 95% confidence interval for the difference of the two proportions would be given (0.115;0.719).  

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 for brand A  

represent the estimated proportion for male

is the sample size required for male

represent the real population proportion for female

represent the estimated proportion for female

is the sample size required for female

represent the critical value for the margin of error  

The population proportion have the following distribution  

Solution to the problem

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

Assuming a confidence level of 95%.

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.  

The standard error for this case is given by:

And replacing into the confidence interval formula we got:  

And the 95% confidence interval for the difference of the two proportions would be given (0.115;0.719).  

 The number of loaves of  banana bread can Javier make with 4 teaspoons of nutmeg is 32.

Step-by-step explanation:  Given that Javier uses teaspoons of nutmeg for each loaf of banana bread he makes.

We are to find the number of loaves of banana bread can Javier make with 4 teaspoons of nutmeg.

We will be using the UNITARY method to solve the given problem.

We have

Number of loaves of bread made by teaspoons of nutmeg = 1.

So, number of loaves of bread made by 1 teaspoon of nutmeg will be

Therefore, the number of loaves of bread made by 4 teaspoon of nutmeg is given by

Thus, the number of loaves of  banana bread can Javier make with 4 teaspoons of nutmeg is 32.