Question

A psychologist is interested in constructing a 90% 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. 69 of the 823 randomly selected people who were surveyed agreed with this theory.

a. With 90% 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 betweenand .

b. If many groups of 823 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

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 69 / 823 = 0.084

1 - = 1 - 0.084 = 0.916

Z/2 = Z0.05 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 (((0.084 * 0.916) / 823)

= 0.016

A 90% confidence interval for population proportion p is ,

± E

= 0.084  ± 0.016

= ( 0.068, 0.100 )

With 90% 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 0.068 and 0.100

b. If many groups of 823 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About 90 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 10 percent will not contain the true population proportion.