Question

Please solve using graphing calculator. Include what is typed into calculator in your explaination. For example:

First, type the data under L1, then go to STAT --> TESTS -->TInverval.

Inpt: Data (highlight the word Data)

List: L1

Freq: 1

C-level .98

Calculate--> (3.54, 4.29)

Show as much work as you can to support answer.

In a Pew Research Center poll 745 randomly selected adults, 589 said that it is morally wrong not to report all income on tax returns. Assume all requirements are satisfied. You can use a calculator function.

1. Construct a 90% confidence interval estimate of the proportion of all adults who said that it is morally wrong not to report all income on tax returns.
2. Construct a 99% confidence interval estimate of the proportion of all adults who said that it is morally wrong not to report all income on tax returns.
3. Compare the confidence intervals from part 1 and part 2 and identify the interval that is wider. Explain why it is wider.

Answer 1

Answer)

steps for the graphing calculator

in case of proportion we use z interval

step 1

First, we need to choose a stat

step 2:

then we need to choose z interval which is on 7

step 3:

then we need to enter the required input data

proportion, sample size, and confidence level

then we need to calculate and interpret to get the required confidence interval.

Confidence interval is given by

[P-MOE, P-MOE]

Where P is the proportion and MOE is margin of error

MOE = Z*Standard error

Z is the critical value for different confidence level and standard error = √p*(1-p)/√n

N = sample size

- 90% confidence interval

Z value for 90% confidence interval ia 1.645

and P here is = 589/745 = 0.79060402684

N = 745

Therefore, required

MOE = 0.02452174882

Therefore, required confidence interval is

[P-MOE, p+MOE]

[ 0.76608227801, 0.81512577567]

-99% confidence interval

Z value for 99% confidence interval is 2.58

Therefore,

MOE = 0.03845964254

Confidence interval

[ 0.75214438430, 0.82906366938]

-

Clearly, 99% confidence interval is wider than 95% confidence interval, because we know that here confidence interval means the percentage of all the possible samples, and here clearly 99% is more than 95%.

And moreover, if we will look at the formula of the margin of error

MOE = z*standard error

The margin of error is directly proportional to the confidence level of critical value.

So larger the confidence level, greater the margin of error, and consequently wider the confidence interval.