Question

psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 68 of the 945 randomly selected people who were surveyed agreed with this theory.Round your answers to two decimal places.A. With 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between _____ and _____.B. If many groups of 945 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About_____ percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about_____ percent will not contain the true population proportion.

Answer 1

Answer:

A.We therefore have with 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between 0.0555 and 0.0884

B. About 95 percent of these confidence intervals will contain the true population of all the people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about 5 percent will not contain the true population

Explanation:

The parameters given are;

The number of persons who accept the theory that a person's spirit is no more than the complicated neurons in the brain, x = 68

The sample size, n = 945

Therefore, we have the confidence interval, CI, given as follows;

$CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

Where:

$\hat p$ = The proportion of persons that agreed with the theory

$\hat p = \dfrac{x}{n} = \dfrac{68}{945} = 0.07196$

z value at 95% confidence level = 1.96

We therefore have;

$CI=0.07196\pm 1.96\times \sqrt{\dfrac{0.07196(1-0.07196)}{945}}$

Which gives the 95% confidence interval as follows;

0.0555 < $\hat p$ < 0.0884

A.We therefore have with 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between 0.0555 and 0.0884

B. About 95 percent of these confidence intervals will contain the true population of all the people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about 5 percent will not contain the true population.