Question

1. The data below is the city gas mileage for a sample of hybrid cars, as reported by the Environmental Protection Agency in 2007.

30, 36, 33, 27, 31, 25, 28, 31, 45 mpg

Construct and interpret a 95% confidence interval for the population mean for the miles per gallon of hybrids. You may assume that the population of gas mileage normally distributed with no outliers. Answer the following:                        

a What is the level of confidence?                           

b. What is your final numeric answer?   

c. . Using the information from the previous question, what is your final answer in the context of the problem in a complete sentence.

2. In August 2003, it was reported that many employed adults in the U.S. agreed that basic mathematical skills were very important to their job. A job placement advisor wants to estimate this proportion so she takes a random sample of 500 employed adults and finds 320 of the feel that basic mathematics skills are very important to their job.   Find a 99% confidence interval for the population proportion of those who reported that math skills were very important to their job.  

a. What is the level of confidence?
b. What critical value would you need to use with this formula?
c. What is your final numeric answer?   

d. Using the information from the previous question, what is your final answer in the context of the problem in a complete sentence

Answer 1

(1)

(a)

the level of confidence = 95%

(b)

n = 9

= 31.7778

s = 5.9325

df = 9 - 1 = 8

From Table,critical values of t = 2.306

Confidence Interval:

So,

Our final numeric answer : (27.218, 36.338)

(c)

Using the information from the previous question, our final answer in the context of the problem in a complete sentence.:

The 95% Confidence Interval (27.218, 36.338) is arange of values we are 95% confident will contain the true unknown population mean of for the miles per gallon of hybrid cars.

(2)

(a)

the level of confidence = 99%

(b)

The critical value we would need to use with this formula = 2.576

(c)

Confidence Interval:

Our final numeric answer: (0.585, 0.695)

(d)

The 99% Confidence Interval (0.585, 0.695) is a range of values we are 99% confident will contain the unknown true population proportion of those who reported that math skills were very important to their job.