08 Jan OBJECTIVE: DETERMINE

Confidence Interval Concepts (graded)

Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you

increase the confidence level,

increase the sample size, or

increase the margin of error? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.

____________________________________________________________________________________________

For few homework questions, additional videos, Excel templates, voice video on excel templates, How to work with ilabs please refer to this webpage

CLICK HERE FOR ALL EXCEL WORKSHEETS AND YOUTUBE LINKS

___________________________________________________________________________________________

PLEASE USE THE Z SCORE FOR THE GIVEN CONFIDENCE LEVEL if you are working the problems by hand.

Here are a few questions that you can participate for discussion points from your study plan on normal distribution. This may help you toward understanding concepts and the quiz for Week 7.

Please see attached excel worksheet for calculations if you are interested.

OBJECTIVE: FIND THE MARGIN OF ERROR

1. Find the margin of error for the given values of c = 0.95 , s= 3.6 and n= 36

(Round to three decimal places as needed)

STUDY PLAN: 6.1.13, 6.1.15

OBJECTIVE: CONSTRUCT AND INTERPRET CONFIDENCE INTERVALS FOR THE POPULATION MEAN

2. You are given the sample mean and the sample standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 37 gas grills has a mean price of $637.70 and a standard deviation of $58.30

(Round to one decimal place as needed)

STUDY PLAN: 6.1.35, 6.1.36, 6.1.37, 6.1.40

OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE

3. A doctor wants to estimate the HDL cholesterol of all 20- to 29- year-old females. How many subjects are needed to estimate the HDL cholesterol within 4 points with 99% confidence assuming standard deviation sigma = 19.4? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required?

(Round to the next whole number)

STUDY PLAN: 6.1.53, 6.1.56

4. A 2011 Gallup Poll found that 76% of Americans believe that high achieving high school students should be recruited to become teachers. This poll was based on a random sample of 1002 Americans.

a. Find a 95% confidence interval for the proportion of Americans who would agree to this.

b. Interpret your result in the context of the given study.

c. Do these data refute a pundit’s claim that 2/3 of Americans believe this statement? Explain.

Taken from Stats Data & Models. De Veaux velleman Bock 4th edition

OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE

5. A researcher wishes to estimate, with 95% confidence, the proportion of adults who have high-speed Internet access. Her estimate must be accurate within 2% of the true proportion.

a. Find the minimum sample size needed, using a prior study that found that 52% of the respondents said they have high-speed Internet access.

(Round to the nearest whole number as needed)

b. What is the minimum sample size needed assuming that no preliminary estimate is available?

STUDY PLAN: 6.3.17, 6.3.18