MATH 221 Week 6 DQ Confidence Interval Concepts

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

OBJECTIVE: FIND A CRITICAL VALUE

4. Find the critical value tc for the confidence level c= 0.80 and sample size n= 17

(Round to the nearest thousandth as needed)

STUDY PLAN: 6.2.1, 6.2.3

OBJECTIVE: CONSTRUCT AND INTERPRET CONFIDENCE INTERVALS FOR THE POPULATION MEAN

5. The monthly incomes for 12 randomly selected people, each with a bachelor’s degree in economics, are shown below.

4450.05 4596.56 4366.72 4455.33 4151.74 3727.63

4283.45 4527.71 4407.26 3946.96 4023.09 4221.67

a. Find the sample mean. (Round to one decimal place as needed)

b. Find the sample standard deviation (Round to one decimal place as needed)

c. Construct the 99% confidence interval for the population mean mu.

STUDY PLAN: 6.2.5, 6.2.7, 6.2.24, 6.3.11, 6.3.13

OBJECTIVE: DETERMINE THE MINIMUM SAMPLE SIZE

6. 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