### Description

## Instructions

## Learn by Doing

Check your progress. Use this activity to assess whether you can:

- Calculate a 95% confidence interval.
- Interpret a 95% confidence interval in context.

Work through this activity to learn how to calculate a 95% confidence interval using the margin of error. Be sure to review the feedback to learn from your mistakes. You have three attempts. Canvas will record your highest score.

Note: the last question in this activity is an essay question. The essay question is not automatically graded; your instructor will enter the points for this question later. WARNING: you will need to enter your response to the essay question with each attempt. __Your instructor will only grade the essay question for your attempt with the highest total score for the remaining questions__.

After you complete this activity, review your answers to the automatically graded questions and use the feedback to improve your score if you did not earn full credit. You have three attempts. Canvas will record your highest score.

## Discussion Board

Use the *Module 16* discussion board (opens in a new tab) to ask questions or provide feedback about the problems in any Module 16 activity – including this quiz.

### Attempt History

Attempt | Time | Score | |
---|---|---|---|

LATEST | Attempt 1 | 19 minutes | 8 out of 10 * |

*** Some questions not yet graded

Correct answers are hidden.

Score for this attempt: **8** out of 10 *

Submitted Mar 19 at 10:54am

This attempt took 19 minutes.

Suppose that a random sample of 100 part-time college students is 68% female. In this activity, we calculate the 95% confidence interval for the proportion of all part-time college students that are female.

Recall that the 95% confidence interval is:** sample proportion ** where

*SE*is the standard error (or standard deviation).

Question 1 2 / 2 pts

First we need to find the standard error.

In the previous module, we met the formula for calculating the standard deviation of the distribution of sampling proportions.

*??**??*=*??*(1?*??*)*??*???????

But we don’t know the population proportion, *p*. So to calculate the standard deviation (a.k.a. the standard error) we estimate the standard error with the sample proportion *??*?

*??**??*?*??*?(1?*??*?)*??*???????

In this scenario we are given that that a random sample of 100 part-time college students is 68% female. So the sample proportion of females is *??*?=0.68*??*=100

Calculate the standard error. Round to three decimal places.

Correct.

*??**??*?*??*?(1?*??*?)*??*???????=0.68(1?0.68)100???????????

Question 22 / 2 pts

Recall that at 95% confidence level the margin of error is calculated as follows.

*margin of error* = 2(*SE*).

What is the margin of error? Do not round.

Correct*. *

*margin of error* = 2(0.047) = 0.094

Question 32 / 2 pts

95% *confidence interval* = *sample proportion* *margin of error*

Calculate the 95% confidence interval.

What is the smallest number from the confidence interval? Enter your answer as a proportion (a decimal number) NOT a percentage. Do not round.

Correct. sample proportion

95% confidence interval = 0.68

Smallest number = 0.68 – 0.094 = 0.586

Question 42 / 2 pts

What is the largest number in your confidence interval? Enter your answer as a proportion (decimal number) NOT a percentage. If necessary, round to three decimal places.

Correct. sample proportion

95% confidence interval = 0.68

Largest number = 0.68 + 0.094 = 0.774

Question 5Not yet graded / 2 pts

State the confidence interval. Then convert the values to percentages and interpret the confidence interval in context.

0.586 < P< 0.774 58.6% to 77.4% % is a confidence and the proportion of smaller students are (females ) so the number is between 50.6% and 77.4%

So I need help with question 5 (attached) I have provided the rest of the questions because the questions are related