Confidence Intervals for Proportions

Confidence Intervals for Proportions:
https://www.wolframalpha.com/input/?i=confidence interval proportion
Hypothesis Testing for Proportions:
https://digitalfirst.bfwpub.com/stats_applet/generic_stats_applet_22_pvalprop. html
Normal Distribution Calculator:
http://onlinestatbook.com/2/calculators/normal_dist.html
Inverse Normal Calculator:
http://onlinestatbook.com/2/calculators/inverse_normal_dist.html

From a study from 2014, approximately 32% of the sample reported usually getting insufficient sleep (as defined as less than 7 hours of sleep on average). The sample consisted of 9,874 randomly selected adults in Washington state.

a. Show that each of the necessary conditions (Randomization Condition, 10% Condition, Success/Failure Condition) are satisfied to construct a confidence interval. Briefly explain how each of the three conditions are satisfied.

b. Find the 97% confidence interval for the proportion of Washington state adults that usually get insufficient sleep.
(To show your work: Write down what values you are entering into the confidence interval calculator.)

c. Explain what your interval from part (b) means. (What exactly does it tell us about Washington adults?)

d. Give the margin of error for the confidence interval from part (b).

2. From a study from earlier this year, it is believed that approximately 7% of U.S. adults do not use the internet. Suppose researchers are doing a study to see if the proportion of Washington state adults that do not use the internet is lower than the reported U.S. adult proportion. The researchers decide to survey 200 randomly selected adults throughout the state of Washington.

a. Define a parameter for hypothesis testing and write the null hypothesis and alternative hypothesis for this study.

b. Show that each of the necessary conditions (Randomization Condition, 10% Condition, Success/Failure Condition) are satisfied to perform a hypothesis test. Briefly explain how each of the three conditions are satisfied.

c. Suppose that after conducting the survey, the researchers find that 11 people in the 200-person sample do not use the internet. Perform the hypothesis test and find the P-value. (To show your work: Write down what values you are entering into the hypothesis testing calculator.)

d. Is there strong evidence that the proportion of people in Washington state that do not use the internet is lower than 7%? Briefly explain how your hypothesis testing results indicates this.