Chapter 7 Section 3

One Must Go!

Citrus Fruits Edition

• Tangelo

• Pomelo

• Caviar Lime

• Clementine

• Yuzu

A company has developed a new type of light bulb and wants to estimate its mean lifetime. Assume the lifetime of this light bulb has a standard deviation of 30 hours. A simple random sample of 100 bulbs had a sample mean lifetime of 750.2 hours. Construct a 90% confidence interval for the population mean lifetime of all bulbs manufactured by this new process.

Are we in Section 1 or Section 2?

• Section 1

• Section 2

• I am unsure

A company has developed a new type of light bulb and wants to estimate its mean lifetime. A simple random sample of 100 bulbs had a sample mean lifetime of 750.2 hours with a sample standard deviation of 34 hours. Construct a 90% confidence interval for the population mean lifetime of all bulbs manufactured by this new process.

• (744.55, 755.85)

• (730.2, 770.2)

• (760.2, 770.2)

• (744.59, 755.81)

A company has developed a new type of light bulb and wants to estimate its mean lifetime. A simple random sample of 100 bulbs had a sample mean lifetime of 750.2 hours with a sample standard deviation of 34 hours. Construct a 90% confidence interval for the population mean lifetime of all bulbs manufactured by this new process.

What is the statement of confidence?

• We are 90% confident that the population mean lifetime is between 744.55 and 755.85

• We are 10% confident that the population mean lifetime is between 744.55 and 755.85

• We are 90% confident that the population mean lifetime is between 748.55 and 759.85

• We are 10% confident that the population mean lifetime is between 748.55 and 759.85

What are the key components needed to construct a confidence interval?

1.    ​ (a)  

2.     A margin of error

a.     ​ (b)   , sometimes called a multiplier, “Z*” (or Z_α/2) or “t*” (or t_α/2) 

b.     Standard error, either​ (c)   when σ is known or ​ ​ (d)   when it is unknown

• A point estimate

• A critical value

Type AB blood is found in only 3% of the population.  There are 250 people chosen at random, and 11 are found to have type AB blood. 

1. What is p? ​ (a)  

2. What is p̂? ​ (b)   ​

• 3%

• 4.4%

• 3

• 4.4

• 3.4%

• 5%

• 250

• 11

An environmental group reports that 70% of a particular state’s population recycles.  A survey conducted found that out of 300 people, only 60% recycle. 

1. What is p? ​ ​ (a)  

2. What is p̂? ​ ​ ​ (b)  

• 3

• 4.4

• 3.4%

• 5%

• 70%

• 60%

• 250

• 300

• 70

An environmental group reports that 70% of a particular state’s population recycles.  A survey conducted found that out of 300 people, only 60% recycle. 

2. What would be x, the number of people out of the sample of 300 who recycle? 

• 120

• 180

• 200

• 240

What is the point estimate for a population proportion? 

• population mean

• sample proportion

• population proportion

• sample median

what is the standard deviation formula for sample proportions?