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. 51 of the 838 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible. 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 838 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.
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. 51 of the 838 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.
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 838 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.
It is given that 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.
a)
The sample proportion is 0.0609(=51/838).
The sample size is 838.
Consider the confidence interval as 90%, the two-tailed z value at 0.10 level of significance is 1.645 .
The 90% confidence interval for the population proportion is calculated as follows:
Thus, 90% confidence 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 is between 0.0474 and 0.0746.
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