Confidence Intervals for Proportions:

www.wolframalpha.com

(Enter "confidence Intervals Proportions" in the search bar)

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

1.In a recent study from pew research Center, approximately 7% of the sample said that they do not use the internet. The sample consisted of 1502 randomly selected U.S. adults

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 98% confidence interval for this sample data. (To show your work: Write down what values your are entering into the confidence interval calculator.)

C. Explain what your interval from part (b) means. (What exactly does it tells us U.S. adults?)

D. Give the Margin of Error for the confidence interval from part (b).

2.According to a past study from 2018 from the City of Seattle, it is believed that 26% of the households in Seattle have an internet capable gaming console. Suppose your are planning to do the follow-up study to understand the current proportion of households in Seattle with internet capable gaming consoles. You suspect that the proportion is probably still close to 26%.

How large should your sample be if you want the Margin of Error to be within 3% with a confidence level of 96% (Be sure to show your Calculations) Keep in mind that the z* value for a confidence level of 96% is 2.054.

3.What effect does each of the following have on the size of confidence interval? That means, for each of the following, does the confidence interval increase in size, decrease in size, approximately the same size?

a. Increasing the size of the sample

b. Decreasing the confidence level

c. Increasing the Margin of error

4.From a study from 2014, it was believed that approximately 32% of adults in Washington state get insufficient sleep (as defined as less than 7 hours of sleep on average) Suppose researchers are doing a study to see if the proportion of Washington adults that get insufficient sleep is lower now. The researcher decide to survey 150 randomly selected adults throughout the state.

A. Define a parameter for hypothesis testing and write the null hypothesis and alternative hypothesis for 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 44 people in the 150-person sample get insufficient sleep. Perform the hypothesis test and find the P-value (To show your work: Write down what values your are entering into the hypothesis testing calculator)

D.Is there strong evidence that the proportion of people in Washington state with insufficient sleep is lower than 32%? Briefly explain how your hypothesis testing results indicates this.