Confidence Intervals

The first step in a confidence interval for proportions involves....

• Stating p = the proportion of _________.

• Stating p-hat = the proportion of _________.

• Calculating the Margin of Error

Check the following that are conditions that need to be verified for confidence intervals for proportions

• Sample is Random

• Sample size is greater than 30

•  $n\left(p-hat\right)\ge5,\ n\left(q-hat\right)\ge5\$  

What is the critical value for a 95% confidence interval?

• $1.645$

• $1.96$

• $2.33$

• $1.5$

I want to know what proportion of HFL seniors have blue eyes. I take a random sample of 100 seniors and 31 have blue eyes. What is my p-hat?

• $0.31$

• $0.2$

• $0.15$

• $0.98$

Calculate the confidence interval if
 $p-hat\ =\ \frac{18}{75}$  Margin of Error =  $0.05$  

•  $\left(17.95,\ 18.05\right)$  

•  $\left(0.19,\ 0.29\right)$  

•  $\left(19,\ 29\right)$  

•  $\left(0.24,\ 0.29\right)$  

What is our confidence interval statement (step #5) if our interval is (0.75, 0.87) at 95% confidence level ?

• There is a 95% chance the true value of p lies between 0.75 and 0.87.

• With 95% confidence the true proportion of_____is between 75% and 87%

Calculate the Margin of Error if  $n=\ 50$  
 $p-hat\ =\ 0.60\$  at 95% confidence level 

•  $0.114$  

•  $0.1358$  

•  $0.25$  

•  $0.009$  

If  $p-hat\ =\ 0.45.$  What is the value of  $q-hat?$  

•  $1.45$  

•  $0.65$  

•  $0.55$  

•  $0.33$  

If  $p-hat\ =\ 0.98.$  What is the value of  $q-hat?$  

•  $0.10$  

•  $1.98$  

•  $0.02$  

•  $0.05$  

A study wants to find the proportion of adults who like cake. 1000 people were surveyed, and 898 people were found to like cake. Calculate a 98% confidence interval.

• $\left(0.876,\ 0.92\right)$

• $\left(0.898,\ 0.955\right)$

• $\left(898,\ 1015\right)$

• $\left(0.80,\ 0.9\right)$