7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample...

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Bluman, Chapter 7 7.3 Confidence Intervals and Sample Size for Proportions p = population proportion (read p “hat”) = sample proportion For a sample proportion, where X = number of sample units that possess the characteristics of interest and n = sample size. 1 1 Friday, January 25, 13

Transcript of 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample...

Page 1: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

7.3 Confidence Intervals and Sample Size for Proportions

p = population proportion (read p “hat”) = sample proportionFor a sample proportion,

where X = number of sample units that possess the characteristics of interest and n = sample size.

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Page 2: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7 2

Test 7 Thursday Jan 17

All Homework due Monday Jan 14; or see me during tutorial Tuesday Jan 15

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Page 3: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

Chapter 7Confidence Intervals and Sample Size

Section 7-3Example 7-8Page #378

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Bluman, Chapter 7

Example 7-8: Air Conditioned Households

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Page 5: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

In a recent survey of 150 households, 54 had central air conditioning. Find and , where is the proportion of households that have central air conditioning.

Since X = 54 and n = 150,

Example 7-8: Air Conditioned Households

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Page 6: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

In a recent survey of 150 households, 54 had central air conditioning. Find and , where is the proportion of households that have central air conditioning.

Since X = 54 and n = 150,

Example 7-8: Air Conditioned Households

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Page 7: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

In a recent survey of 150 households, 54 had central air conditioning. Find and , where is the proportion of households that have central air conditioning.

Since X = 54 and n = 150,

Example 7-8: Air Conditioned Households

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Page 8: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

when np ≥ 5 and nq ≥ 5.

Formula for a Specific Confidence Interval for a Proportion

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Bluman, Chapter 7

when np ≥ 5 and nq ≥ 5.

Formula for a Specific Confidence Interval for a Proportion

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Rounding Rule: Round off to three decimal places.

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Page 10: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

Chapter 7Confidence Intervals and Sample Size

Section 7-3Example 7-9Page #378

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Page 11: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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Page 12: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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Page 13: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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7Friday, January 25, 13

Page 14: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

7

7Friday, January 25, 13

Page 15: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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7Friday, January 25, 13

Page 16: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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Page 17: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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Page 18: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A sample of 500 nursing applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

Example 7-9: Male Nurses

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You can be 90% confident that the percentage of applicants who are men is between 9.6% and 14.4%.

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Bluman, Chapter 7

Chapter 7Confidence Intervals and Sample Size

Section 7-3Example 7-10Page #379

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Page 20: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A survey of 1721 people found that 15.9% of individuals purchase religious books at a Christian bookstore. Find the 95% confidence interval of the true proportion of people who purchase their religious books at a Christian bookstore.

Example 7-10: Religious Books

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Bluman, Chapter 7

A survey of 1721 people found that 15.9% of individuals purchase religious books at a Christian bookstore. Find the 95% confidence interval of the true proportion of people who purchase their religious books at a Christian bookstore.

Example 7-10: Religious Books

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Page 22: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A survey of 1721 people found that 15.9% of individuals purchase religious books at a Christian bookstore. Find the 95% confidence interval of the true proportion of people who purchase their religious books at a Christian bookstore.

Example 7-10: Religious Books

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Page 23: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A survey of 1721 people found that 15.9% of individuals purchase religious books at a Christian bookstore. Find the 95% confidence interval of the true proportion of people who purchase their religious books at a Christian bookstore.

Example 7-10: Religious Books

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Page 24: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A survey of 1721 people found that 15.9% of individuals purchase religious books at a Christian bookstore. Find the 95% confidence interval of the true proportion of people who purchase their religious books at a Christian bookstore.

Example 7-10: Religious Books

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You can say with 95% confidence that the true percentage is between 14.2% and 17.6%.

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Bluman, Chapter 7

If necessary, round up to the next whole number.

Formula for Minimum Sample Size Needed for Interval Estimate of a Population Proportion

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Bluman, Chapter 7

Chapter 7Confidence Intervals and Sample Size

Section 7-3Example 7-11Page #380

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Bluman, Chapter 7

A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

Example 7-11: Home Computers

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Page 28: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

Example 7-11: Home Computers

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Page 29: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

Example 7-11: Home Computers

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Page 30: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

Example 7-11: Home Computers

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Page 31: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

Example 7-11: Home Computers

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The researcher should interview a sample of at least 2305 people.

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Bluman, Chapter 7

Chapter 7Confidence Intervals and Sample Size

Section 7-3Example 7-12Page #380

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Bluman, Chapter 7

Example 7-12: Car Phone Ownership

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Bluman, Chapter 7

The same researcher wishes to estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size necessary.

Since there is no prior knowledge of , statisticians assign the values = 0.5 and = 0.5. The sample size obtained by using these values will be large enough to ensure the specified degree of confidence.

Example 7-12: Car Phone Ownership

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Page 35: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

The same researcher wishes to estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size necessary.

Since there is no prior knowledge of , statisticians assign the values = 0.5 and = 0.5. The sample size obtained by using these values will be large enough to ensure the specified degree of confidence.

Example 7-12: Car Phone Ownership

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Page 36: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

The same researcher wishes to estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size necessary.

Since there is no prior knowledge of , statisticians assign the values = 0.5 and = 0.5. The sample size obtained by using these values will be large enough to ensure the specified degree of confidence.

Example 7-12: Car Phone Ownership

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Page 37: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

The same researcher wishes to estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size necessary.

Since there is no prior knowledge of , statisticians assign the values = 0.5 and = 0.5. The sample size obtained by using these values will be large enough to ensure the specified degree of confidence.

Example 7-12: Car Phone Ownership

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Page 38: 7.3 Confidence Intervals and Sample Size for Proportions · 7.3 Confidence Intervals and Sample Size for Proportions ... Formula for a Specific Confidence Interval for a Proportion

Bluman, Chapter 7

The same researcher wishes to estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size necessary.

Since there is no prior knowledge of , statisticians assign the values = 0.5 and = 0.5. The sample size obtained by using these values will be large enough to ensure the specified degree of confidence.

Example 7-12: Car Phone Ownership

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The researcher should ask at least 273 executives.

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Bluman, Chapter 7

Homework

Sec 7.3 page 382 1,2 and 3-19 every other odd Optional: page 384

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