Please use below as a reference when answering the questions

Consider a yes/no survey with this result, 65% 3% responded yes.

In this lesson we will look at how the margin of error, in this case 3%, is calculated.

When a survey is conducted, usually not everyone in the target population is surveyed.

Only a sample of the population is surveyed.

In order for the results to be responsibly reported, a margin of error must be attached, acknowledging that the result might vary a bit if the whole population were surveyed.

Again, consider the survey result 65% 3%.

Of the sample of people asked, 65% said yes. However, not everyone in the population was asked, so there is error in the result. This error is calculated with a specified level of certainty. In this case, certainty that the actual percentage of yes respondents, if the entire population was asked, would be in the interval 65% 3%, restated 62% to 68%.

This specified level of certainty is calledthe confidence level.

Below is the formula for the Margin of Error for Proportions (percentages).

ZA/2 E denotes the margin of error.

(Z with a subscript of /2, pronounced z alpha over 2) is a z-score based on the specified confidence level.

P(lower case p with a caret symbol on top) denotes the percentage that said yes

U(lower case q with a caret symbol on top) denotes the percentage that said no

n is the sample size

E=ZA/2PQ/N

Pronounced E equals z alpha over 2, times the square root of p-hat times q-hat divided by n, end of square root.

We now need to look at how to use a specified confidence level to determine the correct Z/2 for use in the Margin of Error Formula.

Consider a confidence level of 90%

There is a small table, entitled Common Critical Values, located at the bottom right corner of the Positive z-scores table.

A confidence level of 90%, 0.90 matches up with a critical value of 1.645.

1.645 is theZ/2 we use for a confidence level of 90%.

In the same fashion, from the table, 1.96 is theZ/2 for 95%

and 2.575 is theZ/2 for 99%.

Now complete the following questions, show your work.

Report your answers as confidence intervals in form,like 28% 3.7% in the last example of the lesson.

1) A sample of 820 people were surveyed. 32% said yes.

Construct a 90% confidence interval estimate for the percentage that would say yes, If the entire population could be surveyed.

2) A sample of 645 people were surveyed. 81% said yes.

Construct a 95% confidence interval estimate for the percentage that would say yes, If the entire population could be surveyed.

3) A sample of 1,250 people were surveyed. 63% said yes.

Construct a 99% confidence interval estimate for the percentage that would say yes, If the entire population could be surveyed.

4) A sample of 623 people were surveyed. 21% said yes.

Construct a 95% confidence interval estimate for the percentage that would say yes, if the entire population could be surveyed.